Format: Hardback, 190 pages, height x width: 235x155 mm, 6 Illustrations, black and white; XIV, 190 p. 6 illus.
Series: Mathematical Physics Studies
Pub. Date: 25-Oct-2022
ISBN-13: 9783031122002
This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra.
These criteria allow to extend index theorems to such operator classes.
This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems.
This book is intended for advanced students in mathematical physics and researchers alike.
Preliminaries on Crossed Products.- Besov Spaces for Isometric G-actions.- Quantum Differentiation and Index Theorems.- Duality for Toeplitz Extensions.- Applications to Solid State Systems.
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Format: Hardback, 232 pages, height x width: 235x155 mm, 3 Illustrations, black and white; VIII, 232 p. 3 illus
Series: Cornerstones
Pub. Date: 16-Sep-2022
ISBN-13: 9783031091483
This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Polya-Szego and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis in relation to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students in mathematics and applied mathematics. The second edition of Functional Analysis includes several improvements as well as the addition of supplementary material. Specifically, the coverage of advanced calculus and distribution theory has been completely rewritten and expanded. New proofs, theorems, and applications have been added as well for readers to explore.
Preface.- Distance.- The Integral.- Norms.- Lebesgue Spaces.- Duality.- Sobolev Spaces.-Capacity.- Elliptic Problems.- Appendix: Topics in Calculus.- Epilogue: Historical Notes on Functional Analysis.
Format: Paperback / softback, 62 pages, height x width: 235x155 mm, 25 Tables, color; 14 Illustrations,
color; 2 Illustrations, black and white; VIII, 62 p. 16 illus., 14 illus. in color.
Series: SpringerBriefs in Mathematical Physics 44
Pub. Date: 17-Oct-2022
ISBN-13: 9789811946448
The book addresses a key question in topological field theory and logarithmic conformal field theory: In the case where the underlying modular category is not semisimple, topological field theory appears to suggest that mapping class groups do not only act on the spaces of chiral conformal blocks, which arise from the homomorphism functors in the category, but also act on the spaces that arise from the corresponding derived functors. It is natural to ask whether this is indeed the case. The book carefully approaches this question by first providing a detailed introduction to surfaces and their mapping class groups. Thereafter, it explains how representations of these groups are constructed in topological field theory, using an approach via nets and ribbon graphs. These tools are then used to show that the mapping class groups indeed act on the so-called derived block spaces. Toward the end, the book explains the relation to Hochschild cohomology of Hopf algebras and the modular group.
Mapping class groups.- Tensor categories.- Derived functors.
Format: Hardback, 637 pages, height x width: 235x155 mm, 108 Illustrations,
black and white; X, 637 p. 108 illus.
Series: Monografie Matematyczne 75
Pub. Date: 19-Oct-2022
ISBN-13: 9783031086540
This monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections.
The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists and detailed indices that may lead to expected or unexpected information.
Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research.
1 Norms, Normed spaces, Banach spaces.- 2 Some basic definitions and tools.- 3 Equivalent norms.- 4 Basic differentiability in Banach spaces.- 5 Basic convexity.- 6 Some structural properties of Banach spaces.- 7 The use of Smulyan's tests.- 8 Asplund averaging I.- 9 Tools for renorming.- 10 Renorming of nonseparable Banach spaces .- 11 Examples on C1-smoothness.- 12 Examples on Rotundity.- 13 Nonlinear Transfer Techniques.- 14 Lipschitz functions.- 15 Spaces isomorphic to Hilbert spaces.- 16 Superreflexive spaces.- 17 The Kingdom of Tsirelson's space.- 18 The L(infinity) spaces.- 19 Higher order smoothness.- 20 James boundaries .- 21 RNP property.- 22 SSD spaces.- 23 Norms with MIP.- 24 Nicely smooth Banach spaces.- 25 Weak Hadamard differentiability.- 26 Fabian's farm of Lipschitz Asplund spaces.- 27 Fonf's land of spaces isomorphic to polyhedral spaces.- 28 Hajek's garden of nice functions on c0(gamma).- 29 Kottman-type results.- 30 3-space properties.- 31 Polynomials.- 32 Miscellaneous applications.- 33 Miscellaneous topics.- 34 More on WCG spaces and their relatives.- 35 Valdivia compacta.- 36 Renorming classical spaces.- 37 Symmetric norms.- 38 A concise list of coordinates of the relationship.- 39 Some easily formulated open questions on construction of norms in separable spaces.- Index of figures.
Format: Hardback, 402 pages, height x width: 235x155 mm, 9 Illustrations, black and white; VIII, 402 p. 9 illus.
Series: Developments in Mathematics 77
Pub. Date: 15-Oct-2022
ISBN-13: 9783031116186
This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales.
First proposed by S. Hilger, the time scale theory?a unified view of continuous and discrete analysis?has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains.
As a new and exciting type of mathematics?and more comprehensive and versatile than the traditional theories of differential and difference equations?, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences.
Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
Riemann Integration, Stochastic Calculus and Shift Operators on Time Scales.- -Measurability and Combined Measure Theory on Time Scales .- Shift Invariance and Matched Spaces of Time Scales.- Almost Periodic Functions under Matched Spaces of Time Scales.- Almost Automorphic Functions under Matched Spaces of Time Scales.- C0-Semigroup and Stepanov-like Almost Automorphic Functions on Hybrid Time Scales.- Almost Periodic Dynamic Equations under Matched Spaces.- Almost Automorphic Dynamic Equations under Matched Spaces.- Applications on Dynamics Models under Matched Spaces.
Format: Paperback / softback, 596 pages, height x width: 235x155 mm, 14 Illustrations, color;
131 Illustrations, black and white; X, 596 p. 145 illus., 14 illus. in color.
Series: UNITEXT 139
Pub. Date: 21-Oct-2022
ISBN-13: 9783031094286
This book presents in a compact form the program carried out in introductory statistics courses and discusses some essential topics for research activity, such as Monte Carlo simulation techniques, methods of statistical inference, best fit and analysis of laboratory data. All themes are developed starting from fundamentals, highlighting their applicative aspects, up to the detailed description of several cases particularly relevant for technical and scientific research. The text is dedicated to university students in scientific fields and to all researchers who have to solve practical problems by applying data analysis and simulation procedures. The R software is adopted throughout the book, with a rich library of original programs accessible to the readers through a website.
1 Probability.- 2 Representation of random phenomena.- 3 Basic probability theory.- 4 Multivariate Probability Theory.- 5 Functions of random variables.- 6 Basic statistics: parameter estimation.- 7 Basic statistics: hypothesis testing.- 8 Monte Carlo methods.- 9 Applications of Monte Carlo methods.- 10 Statistical inference and likelihood.- 11 Least squares.- 12 Experimental data analysis.- Appendix A: Table of symbols 533.- Appendix B: R software 535.- Appendix C: Moment-generating functions 539.- Appendix D: Solutions of problems 543.- Appendix E: Tables.
Format: Hardback, 484 pages, height x width: 235x155 mm, 132 Illustrations, color;
12 Illustrations, black and white; VIII, 484 p. 144 illus., 132 illus. in color.
Series: Springer Optimization and Its Applications 196
Pub. Date: 17-Oct-2022
ISBN-13: 9783031105944
Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.
1. Introduction.-2. Divide-and-Conquer.-
3. Dynamic Programming and Shortest Path.-
4. Greedy Algorithm and Spanning Tree.-
5. Incremental Method and Maximum Network Flow.-
6. Linear Programming.-
7. Primal-Dual Methods and Minimum Cost Flow.-
8. NP-hard Problems and Approximation Algorithms.-
9. Restriction and Steiner Tree.-
10. Greedy Approximation and Submodular Optimization.-
11. Relaxation and Rounding.
12. Nonsubmodular Optimization.- Bibliography.