Format: Paperback 556 pages, height x width: 235x155 mm, 6 Illustrations, black and white; X, 556 p. 6 illus.,
Series: Lecture Notes in Mathematics 2355
Pub. Date: 18-Jan-2025
ISBN-13: 9783031716560
This book is concerned with the theory of model representations of linear non-selfadjoint and non-unitary operators. This booming area of functional analysis owes its origins to the fundamental works of M. S. Livic on the theory of characteristic functions, the deep studies of B. S.-Nagy and C. Foias on dilation theory, and also to the LaxPhillips scattering theory. Here, a uniform conceptual approach is developed which organically unites all these theories. New analytic methods are introduced which make it possible to solve some important problems from the theory of spectral representations. Aimed at specialists in functional analysis, the book will also be accessible to senior mathematics students.
1. Local Colligations and Model Representations of Linear Non-Self-Adjoint
Bounded Operators.-
2. Unitary Metric Colligations and Their Model Representations.-
3. Colligations Corresponding to Unbounded Operators and Their Model Representations.-
4. Elements of V.P. Potapov's J -Theory and the Factorization Problem of
J -Contractive Matrix Functions.
Format: Hardback, 280 pages, height x width: 235x155 mm, 21 Illustrations, color; 2 Illustrations, black and white; VI, 280 p. 23 illus., 21 illus. in color.,
Series: Operator Theory: Advances and Applications 306
Pub. Date: 04-Apr-2025
ISBN-13: 9783031804854
This volume, which is dedicated to Yuri Karlovich on the occasion of his 75th birthday, includes biographical material, personal reminiscences, and carefully selected papers.
The contributions constituting the core of this volume are written by mathematicians who have collaborated with Yuri or have been influenced by his vast mathematical work. They are devoted to topics of Yuri Karlovich's work for five decades, starting with his work on singular integral operators with shift, then broadened to include Toeplitz, Wiener-Hopf, Fourier and Mellin convolution and pseudodifferential operators, factorisation of almost periodic matrix functions, and local trajectory methods for the study of algebras of convolution and singular integral operators.
- Part I: Yuri Karlovich and his Work.- Yuri Karlovichs Path in
Mathematics.- List of publications of Yuri Karlovich.- Yuri Karlovich and the
Metamorphosis of Spectra of Singular Integral and Toeplitz Operators.- Banach
Algebras Generated by N Idempotents and Applications.- Part II: Invited
contributions.- M-Local Type Conditions for the C*-Crossed Product and Local
Trajectories.- Factorisation of Symmetric Matrices and Applications in
Gravitational Theories.- Invertibility of Toeplitz Plus Hankel Operators on
??lp-Spaces.- On Pseudodifferential Operators with Slowly Oscillating
Symbols on Variable Lebesgue Spaces with Khvedelidze Weights.- Eigenvalues of
the Laplacian Matrices of Cycles with one Overweighted Edge.- On the Algebra
of Singular Integral Operators with Almost Periodic Coefficients.-
Approximate Reconstruction of a One-Dimensional Parabolic Equation From
Boundary Data.- Characteristic Determinants for a Second Order Difference
Equation on the Half-Line Arising in Hydrodynamics.- On a Singular Integral
Operator with two Shifts and Conjugation.
Format: Hardback, 821 pages, height x width: 235x155 mm, 12 Illustrations, black and white; XII, 819 p.,
Series: Developments in Mathematics 24
Pub. Date: 19-Feb-2025
ISBN-13: 9783031760617
A large mathematical community throughout the world actively works in functional analysis and uses profound techniques from topology. Written by experts in the field, this book is a treasure trove for researchers and graduate students studying the interplay among the areas of point-set and descriptive topology, modern analysis, set theory, topological vector spaces, including Banach spaces, and continuous function spaces. This second edition continues in the same spirit of the acclaimed first edition, providing new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis. It has been expanded by adding completely new Chapters 1721, presenting results concerning, but not limited to, topological spaces and groups with G-bases, various concepts related to networks and their applications in topology and functional analysis, and those that develop topological and analytic methods related to Grothendieck Banach spaces and Boolean algebras with the Nikodym property.
The book will continue to serve as a reference for present and future work done in this area and could serve as a valuable supplement to advanced graduate courses in functional analysis, set-theoretic topology, or the theory of function spaces.
1. Overview.
2. Elementary facts about Baire and Baire-type spaces.
3. K-analytic and quasi-Suslin Spaces.
4. Web-compact spaces and angelic theorems.
5. Strongly web-compact spaces and a closed graph theorem.
6. Weakly analytic spaces.
7. K-analytic Baire spaces.
8. A three-space property for analytic spaces.
9. K-analytic and analytic spaces Cp(X).
10. Precompact sets in (LM)-Spaces and dual metric spaces.
11. Metrizability of compact sets in the class G.
12. Weakly realcompact locally convex spaces.
13. Corsons property (C) and tightness.
14. Frechet-Urysohn spaces and groups.
15. Sequential properties in the class G.
16. Tightness and distinguished Frechet spaces.
17. Distinguished spaces Cp(X) and Delta-spaces X.
18. Generalized metric spaces with G-bases.
19. The Grothendieck property for C(K)-Spaces.
20. The l1-Grothendieck property for C(K)-Spaces.
21. The Nikodym property of Boolean algebras.
22. Banach spaces with many projections.
23. Spaces of continuous functions over compact lines.
24. Compact spaces generated by retractions.
25. Complementably universal Banach spaces.
Format: Hardback, 504 pages, height x width: 240x168 mm, Approx. 505 p.,
Pub. Date: 24-Jan-2025
ISBN-13: 9783031742514
The book covers all the basics of both the topics. The topics are sequenced in such a manner that there is a flow in understanding the advances. The first and second chapters cover all the basic methods and tools for counting. Chapter 3 is on binomial theorem and binomial identities. Topics such as partitions, permutations on multisets, generating functions, recurrence relation, principle of inclusion exclusion, repeated counting, partially ordered sets and Mobius inversion, Polya's counting are covered in different chapters. Some basic chapters have some worked-out exercise. Information on Catalan numbers, Eulerian Numbers, Narayana Numbers, and Schroder Number are given in a chapter. The topic on "discrete probability" covers the connection between counting techniques and probability theory.
There second part of the book covers topics in graph theory such as basics of graphs, trees,bipartite graphs, matching , planar graphs, Euler and Hamilton graphs, graph coloring, Ramsey theory, spectral properties, and some graph algorithms.Adequate exercise and examples are provided so as to enhance the reader's interest and understanding. Some interesting concepts like high hamiltonicity, power of graphs, domination, and matrix tree theorem are introduced.
Basics of Counting.- Induction and Pigeon Hole Principle.- Binomial
Theorem and Binomial Identities Partitions.- Permutations.- Combinations and
Cycles.- Generating Functions.- Recurrence Relations.- Inclusion Exclusion
Principle.- Partial Order and Lattices.- Polyas Theory.- More on Counting.-
Discrete Probability.- Basic Concepts.- Paths Connectedness.- Trees.-
Connectivity.- Eulerian and Hamiltonian Graphs.- Planar Graphs.- Independent
Sets.- Coverings and Matchings.- Graph Coloring.- Ramsey Numbers and Ramsey
Graphs.- Spectral Properties of Graphs.- Directed Graphs and Graph Algorithms.
Format: Hardback, 221 pages, height x width: 235x155 mm, Approx. 220 p.,
Series: Series in Contemporary Mathematics 6
Pub. Date: 12-May-2025
ISBN-13: 9789819795383
Several important problems arising in Physics, Differential Geometry and other topics lead to consider semilinear variational equations of strongly indefinite type and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments and non-degenerate structure, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed.
This book discusses some new abstract methods together with their applications to several localization problems, whose common feature is to involve semilinear partial differential equations with a strongly indefinite structure. This book deals with a variety of partial differential equations, including nonlinear Dirac equation from quantum physics (which is of first order), coupled system of multi-component incongruent diffusion and spinorial Yamabe type equations on spin manifolds. The unified framework in this book covers not only the existence of solutions to these PDEs problems, but also asymptotic behaviors of these solutions. In particular, the results for the nonlinear Dirac equations show several concentration behaviors of semiclassical standing waves under the effect of external potentials and the results for the spinorial Yamabe type equations show the existence of conformal embeddings of the 2-sphere into Euclidean 3-space with prescribed mean curvature.
This book will be appealing to a variety of audiences including researchers, postdocs, and advanced graduate students who are interested in strongly indefinite problems.
Chapter 1. Variational Problems A Brief Retrospective.
Chapter 2. Strongly Indefinite Problems Examples and Motivations.
Chapter 3. Localized Energy Estimates for Strongly Indefinite Functionals.
Chapter 4. Semiclassical Standing Waves of Nonlinear Dirac Equations.
Chapter 5. Effect of External Potentials in a Coupled System Reaction-Diffusion.
Chapter 6. The Spinorial Brezis-Nirenberg Problem.
Chapter 7. Isometrically Embedded Sphere with Prescribed Mean Curvature.-
Chapter 8. Further Problems with Strongly Indefinite Structures.
Format: Hardback, 240 pages
Series: Nankai Tracts in Mathematics 17
Pub. Date: 30-Jan-2025
ISBN-13: 9789811296673
Finsler geometry is a Riemannian geometry without quadratic restriction. It was originated from Riemann's ground-breaking 'Habilitation' address in the year 1854 and has many applications in many fields of the natural sciences including physics, psychology and ecology etc. The book is intended to provide basic materials on Finsler geometry for readers who are interested in Riemann-Finsler geometry, and to bring them into the frontiers of the active research on related topics.The book is comprised of three parts. The first part consists of Chapters 1-4, which cover the basic theory of Finsler geometry and important geometric invariants, including Riemannian quantities and non-Riemannian quantities. Chapters 5-6 present the theory of geodesics and comparison theorems, which are fundamental tools to investigate global Finsler geometry. The last part consisting of Chapters 7-9 presents the recent developments in the global analysis, including harmonic functions, the eigenvalue problem and heat flow etc., on Finsler manifolds although the problems discussed are classical.
Minkowski Spaces
Finsler Manifolds
Connections and Structure Equations
Curvature Invariant Quantities
Theory of Geodesics
Comparison Theorems
Finsler Harmonic Functions
The Eigenvalue Problem
Heat Flow on Finsler Manifolds
Graduates or researchers interested in differential geometry, especially Riemannian?Finsler geometry
Format: Hardback, 224 pages
Pub. Date: 27-Feb-2025
ISBN-13: 9789811297830
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This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered through the text.This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.
Introduction
Review of Sets and Logic
Zermelo?Fraenkel Set Theory
Natural Numbers and Countable Sets
Ordinal Numbers and the Transfinite
Cardinality and the Axiom of Choice
Real Numbers
Models of Set Theory
Ramsey Theory
Upper level undergraduate or beginning graduate students interested in set theory and mathematical logic.
Format: Hardback, 420 pages
Series: Monographs In Number Theory
Pub. Date: 13-Feb-2025
ISBN-13: 9789811280535
This monograph elucidates and extends many theorems and conjectures in analytic number theory and algebraic asymptotic analysis via the natural notions of degree and logexponential degree. The Riemann hypothesis, for example, is equivalent to the statement that the degree of the function (x) - li(x) is ?, where (x) is the prime counting function and li(x) is the logarithmic integral function. Part 1 of the text is a survey of analytic number theory, Part 2 introduces the notion of logexponential degree and uses it to extend results in algebraic asymptotic analysis, and Part 3 applies the results of Part 2 to the various functions that figure most prominently in analytic number theory.Central to the notion of logexponential degree are G H Hardy's logarithmico-exponential functions, which are real functions defined in a neighborhood of that can be built from id, exp, and log using the operations +, ・, /, and °. Such functions are natural benchmarks for the orders of growth of functions in analytic number theory. The main goal of Part 3 is to express the logexponential degree of various functions in analytic number theory in terms of as few 'logexponential primitives' as possible. The logexponential degree of the function epx(1-p) - log x, for example, can be expressed in terms of that of (x) - li(x) and vice versa (where 0.5772 is the Euler-Mascheroni constant), despite the fact that very little is known about the logexponential degree of either function separately, even on condition of the Riemann hypothesis.
A Brief History of Primes
Asymptotic Analysis
The Algebraic Theory of Arithmetic Functions
The Analytic Theory of Arithmetic Functions
Special Functions in Analytic Number Theory
The Analytic Theory of Primes
Logexponential Degree
Real Asymptotic Algebra
Asymptotic Continued Fraction Expansions
The Prime Counting Function (x) and Related Functions
The Riemann Zeta Function (s)
Summatory Functions
Primes in Intervals, the nth Prime, and the nth Prime Gap
Conjectures
Mathematicians or graduate students in mathematics, especially those specializing in analytic number theory or asymtptotic algebra. Sector: academia.