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 Swartz, Charles, 1938
 Singapore : World Scientific Publishing Co. Pte Ltd., ©2018.
 Description
 Software/Multimedia — 1 online resource (302 p.) : ill.
 Summary

"The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz–Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach–Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali–Hahn–Saks Theorem from measure theory and the Hahn–Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis." Provided by publisher.
2. Elementary functional analysis [2009]
 Swartz, Charles, 1938
 New Jersey : World Scientific, c2009.
 Description
 Book — ix, 181 p. ; 24 cm.
 Summary

 Normed Linear and Banach Spaces Linear Operators Quotient Spaces Finite Dimensional Normed Spaces Inner Product and Hilbert Spaces The HahnBanach Theorem Applications of the HahnBanach Theorem to Normed Spaces The Uniform Boundedness Principle Weak Convergence The Open Mapping and Closed Graph Theorems Projections Schauder Basis Transpose and Adjoints of Continuous Linear Operators Compact Operators The Fredholm Alternative The Spectrum of an Operator Subdivisions of the Spectrum The Spectrum of a Compact Operator Symmetric Linear Operators The Spectral Theorem for Compact Symmetric Operators Symmetric Operators with Compact Inverse Bounded Self Adjoint Operators Orthogonal Projections Sesquilinear Functionals The Spectral Theorem for Bounded Self Adjoint Operators An Operational Calculus.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9789814273343 20160604
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA320 .S895 2009  Unknown 
3. Multiplier convergent series [2009]
 Swartz, Charles, 1938
 New Jersey : World Scientific, c2009.
 Description
 Book — x, 253 p. ; 24 cm.
 Summary

 Basic Properties of Multiplier Convergent Series Applications of Multiplier Convergent Series The OrliczPettis Theorem OrliczPettis Theorems for Strong Topology OrliczPettis Theorems for Linear Operators The HahnSchur Theorem Spaces of Multiplier Convergent Series and Multipliers The Antosik Interchange Theorem Automatic Continuity of Matrix Mappings OperatorValued Series and VectorValued Multipliers OrliczPettis Theorems for OperatorValued Series HahnSchur Theorems for OperatorValued Series Automatic Continuity for OperatorValued Matrices.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9789812833877 20160527
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA295 .S93 2009  Unknown 
4. Multiplier convergent series [2009]
 Swartz, Charles, 1938
 Hackensack, N.J. : World Scientific Pub., ©2009.
 Description
 Book — 1 online resource (x, 253 pages)
 Summary

 Introduction
 Basic properties of multiplier convergent series
 Applications of multiplier convergent series
 The OrliczPettis theorem
 OrliczPettis theorems for the strong topology
 OrliczPettis theorems for linear operators
 The HahnSchur theorem
 Spaces of multiplier convergent series and multipliers
 The Antosik interchange theorem
 Automatic continuity of matrix mappings
 Operator valued series and vector valued multipliers
 OrliczPettis theorems for operator valued series
 HahnSchur theorems for operator valued series
 Automatic continuity for operator valued matrices.
 Swartz, Charles, 1938
 Singapore ; River Edge, N.J. : World Scientific Pub. Co., c2001.
 Description
 Book — x, 157 p.
 Summary

 Introduction to the gauge or HenstockKurzweil integral basic properties of the gauge integral Henstock's Lemma and improper integrals the gauge integral over unbounded intervals convergence theorems integration over more general sets Lebesgue measure the space of gauge integrable functions multiple integrals and Fubini's theorem the McShane integral McShane integrability is equivalent to absolute HenstockKurzweil integrability.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9789810242398 20160618
 Swartz, Charles, 1938
 Singapore ; River Edge, N.J. : World Scientific Pub. Co., c1996.
 Description
 Book — xi, 209 p.
 Summary

 The Antosik Mikusinski matrix theorem kconvergence and kboundedness the uniform boundedness principle the BanachSteinhaus theorem continuity and hypocontinuity for bilinear maps Pap's adjoint theorem vector versions of the HahnSchur theorems an abstract HahnSchur theorems the OrliczPettis theorem imbedding co and l sequence spaces.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9789810227364 20160613
 Swartz, Charles, 1938
 Singapore ; River Edge, N.J. : World Scientific Pub. Co., c1994.
 Description
 Book — x, 277 p. : ill.
 Summary

 Part 1 Measure Theory: HewittYosida Decomposition Lebesgue Measure The Nikodym Convergence and Boundedness Theorems.
 Part 2 Integration: Measurable Functions Convergence in Mean Convergence in Measure Comparison of Modes in Convergence The RadonNikodym Theorem The VitaliHahnSaks Theorem.
 Part 3 Differential and Integration: Integrating Derivatives Absolutely Continuous Functions.
 Part 4 Introduction to Functional Analysis: Normed Linear Spaces (NLS) Quotient Spaces The HahnBanach Theorem Ordered Linear Spaces.
 Part 5 Function Spaces: The Space of Finitely Additive Set Functions The Space of Countably Additive Set Functions The Space of Continuous Functions Hilbert Space. (Part contents).
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9789810216108 20160614
8. An introduction to functional analysis [1992]
 Swartz, Charles, 1938
 New York : M. Dekker, c1992.
 Description
 Book — xi, 600 p. : ill. ; 24 cm.
 Summary

Based on an introductory, graduatelevel course given by Swartz at New Mexico State University, this textbook, written for students with a moderate knowledge of point set topology and integration theory, explains the principles and theories of functional analysis and their applications.
(source: Nielsen Book Data) 9780824786434 20160528
 Online
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request 
QA320 .S9 1992  Available 
9. Theories of integration : the integrals of Riemann, Lebesgue, HenstockKurzweil, and McShane [2012]
 Kurtz, Douglas S.
 2nd ed.  Singapore ; Hackensack, NJ : World Scientific, c2012.
 Description
 Book — xv, 294 p. : ill ; 24 cm.
 Summary

 Introduction: Areas Exercises Riemann Integral: Riemann's Definition Basic Properties Cauchy Criterion Darboux's Definition Fundamental Theorem of Calculus Characterizations of Integrability Improper Integrals Exercises Convergence Theorems and the Lebesgue Integral: Lebesgue's Descriptive Definition of the Integral Measure Lebesgue Measure in ℝn Measurable Functions Lebesgue Integral Riemann and Lebesgue Integrals Mikusinski's Characterization of the Lebesgue Integral Fubini's Theorem The Space of Lebesgue Integrable Functions Exercises Fundamental Theorem of Calculus and the Henstock  Kurzweil Integral: Denjoy and Perron Integrals A General Fundamental Theorem of Calculus Basic Properties Unbounded Intervals Henstock's Lemma Absolute Integrability Convergence Theorems Henstock  Kurzweil and Lebesgue Integrals Differentiating Indefinite Integrals Characterizations of Indefinite Integrals The Space of Henstock  Kurzweil Integrable Functions Henstock  Kurzweil Integrals on ℝn Exercises Absolute Integrability and the McShane Integral: Defintions Basic Properties Absolute Integrability Convergence Theorems The McShane Integral as a Set Function The Space of McShane Integrable Functions McShane, Henstock  Kurzweil and Lebesgue Integrals McShane Integrals on ℝn Fubini and Tonelli Theorems McShane, Henstock  Kurzweil and Lebesgue Integrals in ℝn Exercises.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9789814368995 20160614
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA312 .K86 2012  Unknown 
10. Introduction to real analysis [1988]
 DePree, John D., 1933
 New York : Wiley, c1988.
 Description
 Book — xi, 355 p. : ill. ; 24 cm.
 Summary

 Preliminaries. Real Numbers. Sequences. Infinite Series. Euclidean Spaces. Limits of Functions. Continuity and Uniform Continuity. Sequences of Functions. The Riemann Integral Reviewed. The Gauge Integral. The Gauge Integral Over Unbounded Intervals. Convergence Theorems. Multiple Integrals. Convolution and Approximation. Metric Spaces. Topology in Metric Spaces. Continuity. Complete Metric Spaces. Contraction Mappings. The Baire Category Theorem. Compactness. Connectedness. The StoneWeierstrass Theorem. Differentiation of Vectorvalued Functions. Mapping Theorems. Bibliography. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9780471853916 20160528
 Online
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request 
QA331.5 .D46 1988  Available 
11. Matrix methods in analysis [1985]
 Antosik, Piotr.
 Berlin ; New York : SpringerVerlag, 1985.
 Description
 Book — iv, 114 p. ; 25 cm.
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Serials  
Shelved by Series title V.1113  Unknown 
12. Functional calculi [electronic resource] [2013]
 Bosch Giral, Carlos.
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2013.
 Description
 Book — x, 216 p.
 Summary

 Vector and Operator Valued Measures Functions of a Self Adjoint Operator Functions of Several Commuting Self Adjoint Operators The Spectral Theorem for Normal Operators Integrating Vector Valued Functions An Abstract Functional Calculus The Riesz Operational Calculus Weyl's Functional Calculus Appendices: The Orlicz  Pettis Theorem The Spectrum of an Operator Self Adjoint, Normal and Unitary Operators Sesquilinear Functionals Tempered Distributions and the Fourier Transform.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9789814415972 20160611
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