Format: 542 pages, height x width: 235x155 mm, X, 542 p., 1 Hardback
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 76
Pub. Date: 09-Jan-2024
ISBN-13: 9783031465970
This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
11 Singular integral operators.- 12 Dyadic operators and the T (1)
theorem.- 13 The Fourier transform and multipliers.- 14 Function spaces.- 15
Bounded imaginary powers.- 16 The H-functional calculus revisited.- 17
Maximal regularity.- 18 Nonlinear parabolic evolution equations in critical
spaces.- Appendix Q: Questions.- Appendix K: Semigroup theory revisited.-
Appendix L: The trace method for real interpolation theory.
Format: 256 pages, height x width: 235x155 mm, 10 Tables, color; 1 Illustrations, color;
9 Illustrations, black and white; XI, 256 p. 10 illus., 1 illus. in color., 1 Hardback
Series: Infosys Science Foundation Series
Pub. Date: 01-Jan-2024
ISBN-13: 9789819971107
This book provides an insight into the geometric aspects of the spaces of operators studied by using the notion of BirkhoffJames orthogonality. It studies the norm attainment set of an operator and its properties, the notion of which plays a very important role in the characterization of B-J orthogonality of operators. The structure of the norm attainment set is studied for Hilbert space operators and is yet to be understood completely for operators between Banach spaces. The book explores the interrelation between B-J orthogonality in the ground space and in the space of operators in its fullest generality. The book further explores the concept of approximate B-J orthogonality and investigated its geometry both in the ground space as well as in the space of operators. It highlights important geometric properties like smoothness and k-smoothness of bounded linear operators, extreme contractions and symmetricity of bounded linear operators defined between Hilbert spaces as well as Banach spaces.
1 Notations and Terminologies.- 2 Basic theory of B-J orthogonality in
Banach space.- 3 Operator norm attainment.- 4 B-J orthogonality of
operators.- 5 Approximate B-J orthogonality.- 6 Smoothness and ksmoothness
of operators.- 7 Symmetry of the B-J orthogonality.- 8 Extreme contractions.
Format: 72 pages, height x width: 279x210 mm, 13 Illustrations, color; IV, 72 p. 13 illus. in color., 1 Hardback
Pub. Date: 07-Jan-2024
ISBN-13: 9783031474828
This study guide is designed for students taking a Calculus III course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes linear algebra and analytical geometry; lines, surfaces, and vector functions in three-dimensional coordinate systems; multiple-variable functions; multiple integrals and their applications; line integrals and their applications. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses.
Problems: Multivariable Functions.- Solutions of Problems: Multivariable
Functions.- Problems: Lines, Surfaces, and Vector Functions.- Solutions of
Problems: Lines, Surfaces, and Vector Functions.- Problems: Multivariable
Integrals.- Solutions of Problems: Multivariable Integrals.- Problems: Vector
Fields and Line and Surface Integrals.- Solutions of Problems: Vector Fields
and Line and Surface Integrals.- Problems: Vectors and Vector-valued
Functions.- Solutions of Problems: Vectors and Vector-valued Functions.
Format: 435 pages, height x width: 235x155 mm, 37 Illustrations, black and
white; XII, 435 p. 37 illus., 1 Hardback
Series: Developments in Mathematics 78
Pub. Date: 28-Dec-2023
ISBN-13: 9783031454172
The monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.
General definitions and notation.- Boundary behavior of mappings with
Poletsky inequality.- Removability of singularities of generalized
quasiisometries.- Normal families of generalized quasiisometries.- On
boundary behavior of mappings with Poletsky inequality in terms of prime
ends.- Local and boundary behavior of mappings on Riemannian manifolds.-
Local and boundary behavior of maps in metric spaces.- On
Sokhotski-Casorati-Weierstrass theorem on metric spaces.- On boundary
extension of mappings in metric spaces in the terms of prime ends.- On the
openness and discreteness of mappings with the inverse Poletsky inequality.-
Equicontinuity and isolated singularities of mappings with the inverse
Poletsky inequality.- Equicontinuity of families of mappings with the inverse
Poletsky inequality in terms of prime ends.- Logarithmic HOolder continuous
mappings and Beltrami equation.- On logarithmic HOolder continuity of
mappings on the boundary.- The Poletsky and VOaisOalOa inequalities for the
mappings with (p;q)-distortion.- An analog of the VOaisOalOa inequality for
surfaces.- Modular inequalities on Riemannian surfaces.- On the local and
boundary behavior of mappings of factor spaces.- References.- Index.
Format: 918 pages, height x width: 235x155 mm, 25 Illustrations, color; 14 Illustrations,
black and white; X, 918 p. 39 illus., 25 illus. in color., 1 Hardback
Series: Probability Theory and Stochastic Modelling 105
Pub. Date: 08-Jan-2024
ISBN-13: 9783031454639
Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.
In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach spacea unique feature of its content.
Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees.
While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.
Preface.- Notation Index.- Part I. Basics and Marginal Quantization.-
1. Optimal and Stationary Quantizers.-
2. The Finite-Dimensional Setting I.-
3. The Finite-Dimensional Setting II.- Part II. Functional Quantization.-
4. Functional Quantization, Small Ball Probabilities, Metric Entropy and Series
Expansions for Gaussian Processes.-
5. Spectral Methods for Gaussian Processes.-
6. Geometry of Optimal and Rate-Optimal Quantizers for Gaussian Processes.-
7. Mean Regular Processes.- Part III. Algorithmic Aspects and Applications:-
8. Optimal Quantization from the Numerical Side (Static).-
9. Applications: Quantization-Based Cubature Formulas.-
10. Quantization-Based Numerical Schemes.- Appendices.- A. Radon Random Vectors, Stochastic
Processes and Inequalities.- B. Miscellany.- References.- Index.
Format: 290 pages, height x width: 235x155 mm, 13 Illustrations, color;
11 Illustrations, black and white; X, 290 p. 24 illus., 13 illus. in color., 1 Hardback
Series: Springer Optimization and Its Applications 207
Pub. Date: 22-Jan-2024
ISBN-13: 9783031464867
This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardys inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Preface
On a version of Jensen-Steffensen inequality and a note on inequalities in
several variablesShoshana Abramovich
A class of dynamic unilateral contact problems with sub-differential friction law
Oanh Chau, Adrien Petrov, and Arnaud Heibig
Square-free values of $[ \textrm{n}^c \tan^\theta(\log \textrm{n})]$
S. I. Dimitrov
Ostrowski and Trapezoid Type Inequalities for Riemann-Liouville Fractional
Integrals of Functions with Bounded Variation
Silvestru Sever Dragomir
A strong maximum principle for general nonlinear operators
Lucas Fresse and Viorica V. Motreanu
On the Application of Ergodic Theory to an Alternating Series Expansion for
Real Numbers
Chryssoula Ganatsiou and Ilias K. Savvas
Bounds for Similarity Condition Numbers of Unbounded Operators
Michael Gil
Legendre's Geometry and Trigonometry at the Evelpides School (Central
Military School) during the Kapodristrian period
Andreas Kastanis
The Overshadowing of Euclids Geometry by Legendres Geometrie in the Modern
Greek Education
Nikos Kastanis
Finite Element Methods with Higher Order PolynomialsKonstantina C. Kyriakoudi
and Michail A. Xenos
On Local Asymptotics for Orthonormal Polynomials
Eli Levin and D. S. Lubinsky
New Trends in Geometric Function Theory
Khalida Inayat Noor and Mohsan Raza
A unified approach to extended general quasi variational inclusions
Muhammad Aslam Noor, Khalida Inayat Noor and Michael Th. Rassias
On a Reverse Hilbert-Type Inequality in the Whole Plane with
Multi-Parameters
Michael Th. Rassias, Bicheng Yang, Andrei Raigorodskii
Generating functions for the Fubini type polynomials and their applications
Yilmaz Simsek and Neslihan Kilar
Kleene Fixed Point Theorems and Applications
Mihai Turinici
On ergodic states, spontaneous symmetry breaking and quasi-averages
Walter F. Wreszinski and Valentin A. Zagrebnov
Improvement of the Hardy inequality and Legendre polynomials
Nikolaos B. Zographopoulos