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 Alpay, Daniel.
 1st ed.  Basel : Springer, 2007.
 Description
 Book — 1 online resource (331 pages)
 Summary

 The Transformation of Issai Schur and Related Topics in an Indefinite Setting. A Truncated Matricial Moment Problem on a Finite Interval. The Case of an Odd Number of Prescribed Moments. On the Irreducibility of a Class of Homogeneous Operators. Canonical Forms for Symmetric and Skewsymmetric Quaternionic Matrix Pencils. Algorithms to Solve Hierarchically Semiseparable Systems. Unbounded Normal Algebras and Spaces of Fractions.
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2. A complex analysis problem book [2016]
 Alpay, Daniel, author.
 2nd ed.  Cham : Birkhäuser, ©2016.
 Description
 Book — 1 online resource (x, 596 pages) Digital: text file; PDF.
 Summary

 Part I Complex Numbers. Complex Numbers: Algebra. Complex Numbers: Geometry. Complex Numbers and Analysis. Part II Functions of a Complex Variable. CauchyRiemann Equations and Cdifferentiable Functions. Cauchy'sTheorem. Morera, Liouville, Schwarz, et les autres: First Applications. Laurent Expansions, Residues, Singularities and Applications. Computations of Definite Integrals Using the Residue Theorem. Part III Applications and More Advanced Topics. Harmonic Functions. Conformal Mappings. A Taste of Linear System Theory and Signal Processing. Rational Functions. Special Functions and Transforms. Part IV Appendix. Some Topology. Some Functional Analysis Essentials. A Brief Survey of Integration.
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3. Slice hyperholomorphic Schur analysis [2016]
 Alpay, Daniel, author.
 Cham : Birkhäuser, Springer International Publishing, [2016]
 Description
 Book — xii, 362 pages ; 25 cm.
 Summary

 Prologue
 Classical Schur analysis
 Preliminaries
 Some history
 Krein spaces, Pontryagin spaces, and negative squares
 The Wiener algebra
 The Nehari extension problem
 The CarathéodoryToeplitz extension problem
 Various classes of functions and realization theorems
 Rational functions
 Rational functions and minimal realizations
 Minimal factorization
 Rational functions Junitary on the imaginary line
 Rational functions Junitary on the unit circle
 Schur analysis
 The Schur algorithm
 Interpolation problems
 Firstorder discrete systems
 The Schur algorithm and reproducing kernel spaces
 Quaternionic analysis
 Finitedimensional Preliminaries
 Some preliminaries on quaternions
 Polynomials with quaternionic coefficients
 Matrices with quaternionic entries
 Matrix equations
 Quaternionic functional analysis
 Quaternionic locally convex linear spaces
 Quaternionic inner product spaces
 Quaternionic Hilbert spaces : main properties
 Partial majorants
 Majorant topologies and inner product spaces
 Quaternionic Hilbert spaces : weak topology
 Quaternionic Pontryagin spaces
 Quaternionic Krein spaces
 Positive definite functions and reproducing kernel quaternionic Hilbert spaces
 Negative squares and reproducing kernel quaternionic Pontryagin spaces
 Slice hyperholomorphic functions
 The scalar case
 The Hardy space of the unit ball
 Blaschke products (unit ball case)
 The Wiener algebra
 The Hardy space of the open halfspace
 Blaschke products (halfspace case)
 Operatorvalued slice hyperholomorphic functions
 Definition and main properties
 Sspectrum and Sresolvent operator
 Functional calculus
 Two results on slice hyperholomorphic extension
 Slice hyperholomorphic kernels
 The space H²H ̣(B) and slice backwardshift invariant subspaces
 Quaternionic schur analysis
 Reproducing kernel spaces and realizations
 Classes of functions
 The PotapovGinzburg transform
 Schur and generalized Schur functions of the ball
 Contractive multipliers, inner multipliers and BeurlingLax theorem
 A theorem on convergence of Schur multipliers
 The structure theorem
 Carathéodory and generalized Carathéodory functions
 Schur and generalized Schur functions of the halfspace
 Herglotz and generalized Herglotz functions
 Rational slice hyperholomorphic functions
 Definition and first properties
 Minimal realizations
 Realizations of unitary rational functions
 Rational slice hyperholomorphic functions
 Linear fractional transformation
 Backwardshift operators
 First applications : scalar interpolation and firstorder discrete systems
 The Schur algorithm
 A particular case
 The reproducing kernel method
 CarathéodoryFejér interpolation
 Boundary interpolation
 Firstorder discrete linear systems
 Discrete systems : the rational case
 Interpolation : operatorvalued Case
 Formulation of the interpolation problems
 The problem IP(H²H(B)) : the nondegenerate case
 Lefttangential interpolation in ... S(H₁, H₂, B)
 Interpolation in S(H₁, H₂, B) : the nondegenerate case
 Interpolation : the case of a finite number of interpolating conditions
 Leech's theorem
 Interpolation in S(H₁, H₂, B) : Nondegenerate case : Sufficiency
 Epilogue
 Bibliography
 Index
 Notation index.
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QA331.7 .A47 2016  Unknown 
 Alpay, Daniel, author.
 Cham : Birkhauser, [2015]
 Description
 Book — ix, 521 pages ; 25 cm
 Summary

 Prologue. Part I, Analytic functions.
 1 Some algebra.
 2 Exercises in complex variables. Part II, Topology and functional analysis.
 3 Topological spaces.
 4 Normed spaces.
 5 Locally convex topological vector spaces.
 6 Some functional analysis. Part III, Hilbert spaces of analytic functions.
 7 Reproducing kernel Hilbert spaces.
 8 Hardy spaces.
 9 de BrangesRovnyak spaces.
 10 Bergman spaces.
 11 Fock spaces. Index. Name index. Notation index.
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QA320 .A469 2015  Unknown 
 Alpay, Daniel author.
 Cham ; New York : Springer, [2014]
 Description
 Book — xv, 95 pages : illustrations (some color) ; 24 cm.
 Summary

 1. Bicomplex and hyperbolic numbers.
 2. Bicomplex functions and matrices.
 3. BCmodules.
 4. Norms and inner products on BCmodules.
 5. Linear functionals and linear operators on BCmodules.
 6. Schur analysis.
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QA320 .A47 2014  Unknown 
 Alpay, Daniel.
 Basel : Birkhäuser, c2011.
 Description
 Book — 1 online resource (x, 526 p.)
 Online

 dx.doi.org SpringerLink
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 Alpay, Daniel.
 Basel : Birkhäuser Basel, 2003.
 Description
 Book — 1 online resource (XV, 344 pages).
 Summary

 Realization of Functions into the Symmetrised Bidisc
 A Basic Interpolation Problem for Generalized Schur Functions and Coisometric Realizations
 Formal Reproducing Kernel Hilbert Spaces: The Commutative and Noncommutative Settings
 On Realizations of Rational Matrix Functions of Several Complex Variables II
 Bergman Projection and Weighted Holomorphic Functions
 Linear Fractional Transformations, Riccati Equations and Bitangential Interpolation, Revisited
 A Class of Matrixvalued Schrödinger Operators with Prescribed Finiteband Spectra
 Laplace Transforms Asymptotics, Bergman Kernels and Composition Operators
 On the Structure of Selfsimilar Systems: A Hilbert Space Approach
 Reproducing Kernels and a Family of Bounded Linear Operators
 Multipliers in the Reproducing Kernel Hilbert Space, Subnormality and Noncommutative Complex Analysis
 Existence of Unitary Dilations as a Moment Problem.
 Alpay, Daniel.
 Basel : Birkhäuser Basel : Imprint : Birkhäuser, 2002.
 Description
 Book — 1 online resource (XII, 414 pages).
 Summary

 Looking Back
 List of Publications of Harry Dym
 On Joint Work with Harry Dym
 Methods of Krein Space Operator Theory
 Notes on Interpolation in the Generalized Schur Class. I. Applications of Realization Theory
 Stable Dissipative Linear Stationary Dynamical Scattering Systems
 Concrete Interpolation of Meromorphic Matrix Functions on Riemann Surfaces
 On Realizations of Rational Matrix Functions of Several Complex Variables
 The Poincaré
 Hardy Inequality on the Complement of a Cantor Set
 Finite Section Method for Linear Ordinary Differential Equations on the Full Line
 On the Spectral Radius of MultiMatrix Functions
 A Generic Schur Function is an Inner One
 Abstract Interpolation Scheme for Harmonic Functions
 Chains of SpaceTime Open Systems and DNA
 A Class of Robustness Problems in Matrix Analysis
 Dual Discrete Canonical Systems and Dual Orthogonal Polynomials
 NonSelfadjoint SturmLiouville Operators with Multiple Spectra.
 Alpay, Daniel.
 Basel : Birkhäuser Basel : Imprint : Birkhäuser, 2001.
 Description
 Book — 1 online resource (XI, 567 pages).
 Summary

 List of Publications of M.S. Livšic
 Vortices of 2D Systems
 Realization and Factorization in Reproducing Kernel Pontryagin Spaces
 Models of Contractions Constructed from the Defect Function of Their Characteristic Functions
 Measure Schur Complements and Spectral Functions of Unitary Operators with Respect to Different Scales
 On the Second Order Interpolation for Rational Vector Functions
 Generalized Moments, Centerfocus Conditions, and Compositions of Polynomials
 Inverse Spectral Problem for the SturmLiouville Operator with Eigenvalue Parameter Dependent Boundary Condition
 A Module Approach to Commutant Lifting on Kre?n Spaces
 On Dual Canonical Systems and Dual Matrix String Equations
 Angle between Subspaces of Analytic and Antianalytic Functions in Weighted L2 Spaces on the Boundary of a Multiply Connected Domain
 Bitangential Interpolation for Upper Triangular Operators with Infinitely Many Interpolation Nodes
 Some Applications of Operatorvalued Herglotz Functions
 Analogues of a Theorem of Frostman on Linear Fractional Transformations of Inner Functions and the Typical Spectral Structure of Analytic Families of Weak Contractions
 Right and Left Joint System Representation of a Rational Matrix Function in General Position (System Representation Theory for Dummies)
 Oneparameter Semigroups of Fractionallinear Transformations
 Scattering from an Impurity: LaxPhillips Approach
 Spectral Theory of WienerHopf Operators and Functional Model
 Operator Dilations with Prescribed Commutators
 Condition of Orthogonality of Spectral Matrix Function
 Functional Models of Linear Operators
 Nonselfadjoint Periodic Dirac Operators
 A Note on Hyponormal Operators Associated with Quadrature Domains
 Two Remarks on Fuchsian Groups of Widom Type
 A Functional Model for the Lie Algebra SL(2, ?) of Linear Nonselfadjoint Operators.
 Algorithme de Schur, espaces à noyau reproduisant et théorie des systèmes. English
 Alpay, Daniel.
 Providence, R.I. : American Mathematical Society, c2001.
 Description
 Book — viii, 150 p. : ill. ; 26 cm.
 Summary

 Introduction Reproducing kernel spaces Theory of linear systems Schur algorithm and inverse scattering problem Operator models Interpolation The indefinite case The nonstationary case Riemann surfaces Conclusion Bibliography Index.
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QA322.4 .A3913 2001  Available 
 Alpay, Daniel.
 Basel : Birkhäuser Basel : Imprint : Birkhäuser, 1997.
 Description
 Book — 1 online resource.
 Summary

Generalized Schur functions are scalar or operatorvalued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, KreinLanger factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is selfcontained and streamlined so that the indefinite case is handled completely parallel to the definite case.
12. Operator theory [2015]
 Basel : SpringerReference, 2015.
 Description
 Book — 1 online resource : illustrations (some color)
 Summary

 Indefinite Hamiltonian Systems. Locally Definitizable Operators: The Local Structure of Spectrum. Multivalued Operators/Linear Relations Between Krein Spaces. Reproducing Kernel Krein Spaces. Schur Analysis in an Indefinite Setting. Symmetric and Isometric Relations. The Algebraic Ricatti Equation and Its Role in Indefinite Inner Product Spaces. The Critical Point Infinity Associated with Indefinite SturmLiouville Problems. A Von Neumann Algebra over the Adele Ring and the Euler Totient Function. Arithmetic Functions in Harmonic Analysis and Operator Theory. Unbounded Operators, Lie Algebras, and Local Representations. Linear Transforms in Signal and Optical Systems. Realization of HerglotzNevanlinna Functions by Conservative Systems. Robust Stabilization of Linear Control Systems Using A Frequency Domain Approach. SemiSeparable Systems: Representations, Inversion, and Limiting Behavior. Synchronization Problems for Spatially Invariant Infinite Dimensional Linear Systems. Commutative Dilation Theory. Operator Theory and Function Theory in DruryArveson Space and Its Quotients. Taylor Functional Calculus. Sampling Theory and Reproducing Kernel Hilbert Spaces. Quaternionic Analysis: Application to Boundary Value Problems. An Introduction to Hilbert Module Approach to Multivariable Operator Theory. Applications of Hilbert Module Approach to Multivariable Operator Theory. Perturbations of Unbounded Fredholm Linear Operators in Banach Spaces.
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 Basel ; Boston : Birkhäuser Verlag, c2006.
 Description
 Book — xi, 190 p. ; 24 cm.
 Summary

 Editorial Introduction. Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces. Metric Dependent Clifford Analysis with Applications to Wavelet Analysis. A Hierarchical SemiSeparable MoorePenrose Equation Solver. Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics. Noncommutative Trigonometry. Stationary Random Fields over Graphs. Matrix Representations and Numerical Computations of Wavelet Multipliers. Clifford algebravalued Admissible Wavelets.
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QA199 .W38 2006  Available 
14. Reproducing kernel spaces and applications [2003]
 Boston, MA : Birkhauser Verlag, 2003.
 Description
 Book — xv, 344 p. : some ill. ; 24 cm.
 Summary

 Contributions by J. Agler, F.B. Yeh and N.J. Young, D. Alpay, T.Ya. Azizov, A. Dijksma, H. Langer and G. Wanjala, J.A. Ball and V. Vinnikov, M.F. Bessmertnyi, D. Chang, R. Gilbert and J. Tie, H. Dym, F. Gesztesy and L. Sakhnovich, T. Kriete, M. Mboup, S. Saitoh, F. Szafraniec, F. Vasilescu.
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QA331 .R47 2003  Unknown 
 Boston : Birkhäuser Verlag, 1997.
 Description
 Book — 229 p.
 Summary

Generalized Schur functions are scalar or operatorvalued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproduced kernal Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, KreinLanger factorizations, and other topics. This text is intended for students and researchers in mathematics and engineering. An introductory chapter contains background material, including reproducing kernal Pontryagin spaces, complementary spaces in the sense of de Branges, and a result on defining operators as closures of linear relations. The presentation is such that the indefinite case is handled parallel to the definite case.
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QA322 .S37 1997  Available 
 Basel ; Boston : Birkhäuser Verlag, c2006.
 Description
 Book — xi, 190 p.
 Cham : Birkhäuser, [2015]
 Description
 Book — ix, 394 pages : illustrations (some color) ; 25 cm.
 Summary

 Editorial Introduction.
 Part 1: Biographical Material and List of Publications of L.A. Sakhnovich. L.A. Sakhnovich  Biography. List of Publications of L.A. Sakhnovich. L.A. Sakhnovich My Teachers and Studies.
 Part 2: Reserach Papers. D. Alpay, F. Colombo and I. Sabadini: Inner Product Spaces and Krein Spaces in the Quaternionic Setting. D. Alpay, P. Jorgensen, I. Lewkowicz and I. Martziano: Infinite Product Representations for Kernels and Iterations of Functions. Y. Arlinskii and S. Hassi: Qfunctions and Boundary Triplets of Nonnegative Operators. S. Boiko, V. Dubovoy and A. Kheifets: On Some Special Cases of the RadonNikodym Theorem for Vector and Operatorvalued Measures. A.E. Frazho, S. ter Horst and M.A. Kaashoek: State Space Formulas for a Suboptimal Rational Leech Problem II: Parametrization of All Solutions. B. Fritzsche, B. Kirstein and C. Madler: On a Simultaneous Approach to the Even and Odd Truncated Matricial Hamburger Moment Problems. F. Gesztesy and R. Nichols: A JostPaistype Reduction of (Modified) Fredholm Determinants for Semiseparable Operators in Infinite Dimensions. K.A. Makarov and E. Tsekanovskii: On the Addition and Multiplication Theorems. J. Rovnyak and L.A. Sakhnovich: On Indefinite Cases of Operator Identities Which Arise in Interpolation Theory. II. A. Sakhnovich and L. Sakhnovich: Nonlinear FokkerPlanck Equation: Stability, Distance and the Corresponding Extremal Problem in the Spatially Inhomogeneous Case.
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QA329 .R43 2015  Unknown 
 Basel ; New York : Birkhäuser, c2012.
 Description
 Book — 300 p. ; 24 cm.
 Summary

The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schurtype algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrixvalued Caratheodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
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QA371 .I58 2012  Unknown 
19. Operator theory, systems theory, and scattering theory : multidimensional generalizations [2005]
 Boston : Birkhäuser, 2005.
 Description
 Book — xvi, 310 p. : ill. ; 24 cm.
 Summary

 Functional Models for Representations of the Cuntz Algebra. Relations on Noncommutative Variables and Associated Orthogonal Polynomials. Functions of Several Variables in the Theory of Finite Linear Structures Part I: Analysis. Operator Method for Solution of PDEs Based on Their Symmetries. On the Bessmertny? Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes. Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functions II. Preservation of the Norms of Linear Operators Acting on Some Quaternionic Function Spaces. Hardy Algebras Associated with W*Correspondences (Point Evaluation and Schur Class Functions). Notes on Generalized Lemniscates. OneSided Tangential Interpolation for HilbertSchmidt Operator Functions with Symmetries on the Bidisk. Favard's Theorem Modulo an Ideal.
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QA329.2 .O64 2005  Available 
 Cham, Switzerland : Birkhäuser, Springer International Publishing AG, [2018]
 Description
 Book — xvi, 495 pages : illustrations (some color) ; 25 cm.
 Summary

 Editorial introduction / D. Alpay and B. Kirstein
 Biographical material
 List of publications of professor Dr. Dr. h.c. mult : Heinz Langer
 Some pictures from the ceremony
 Heinz Langer : pioneer of operator theory in indefinite inner product spaces / B. Kirstein
 Papers
 The inverse monodromy problem / D.Z. Arov and H. Dym
 The bitangential matrix nevanlinnapick interpolation problem revisited / J.A. Ball and V. Bolotnikov
 Finite rank perturbations in pontryagin spaces and a sturmliouville problem with ... rational boundary conditions / J. Behrndt and F. Philipp
 On unimodular transformations of conservative Lsystems / S. Belyi, K.A. Makarov and E. Tsekanovskiĭ
 Spectral theory of stationary random fields and their generalizations : a short historical survey / G. Berschneider and Z. Sasvári
 Semicircularlike, and semicircular laws induced by certain C*probability spaces over the finite adele ring ... / I. Cho and P.E.T. Jorgensen
 On the asymptotic behaviour of the zeros of the solutions of a functionaldifferential equation with rescaling / G. Derfel, P.J. Grabner and R.F. Tichy
 Rational q x q carathéodory functions and central nonnegative hermitian measures / B. Fritzsche, B. Kirstein and C. Mädler
 On the spectrum of an operator in truncated fock space / O.O. Ibrogimov and C. Tretter
 Limit properties of eigenvalues in spectral gaps / S. Hassi, H.S.V. de Snoo and H. Winkler
 Selfadjoint boundary conditions for the prolate spheroid differential operator / V. Katsnelson
 An addendum to a paper by Li and Zhang / L. Klotz and C. Mädler
 On accelerants and their analogs, and on the characterization of the rectangular weyl functions for dirac systems with locally squareintegrable potentials on a semiaxis / A. Sakhnovich
 Dirac equation : the stationary and dynamical scattering problems / L. Sakhnovich
 Compressed resolvents, Qfunctions and horesolvents in almost pontryagin spaces / H. de Snoo and H. Woracek
 Dissymmetrising inner product spaces / F.H. Szafraniec.
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QA300 .I483 2018  Unknown 
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