Format: Paperback / softback, 182 pages, height x width: 235x155 mm, 25 Illustrations, black and white; VIII, 182 p. 25 illus., 1 Paperback / softback
Series: Lecture Notes of the Unione Matematica Italiana 30
Pub. Date: 24-Aug-2025
ISBN-13: 9783031948817
The aim of the book is to give an introduction to the main concepts in modern dynamics. The Herman Theorem on rigidity of circle di eomoprhisms is used to achieve this goal. Indeed, we reprove this sophisticated theorem with modern techniques involving renormalization and, in the meantime, discuss most of the important concepts used in dynamics. The one-dimensional context of the Herman Theorem reduces the technical di culties and allows to present tools and theories to students with modest background. The book can definitely be used on Master's level.
Chapter 1. Introduction.
Chapter 2. Topology of Circle Homeomorphisms.-
Chapter 3. Topology of Circle Diffeomorphisms.
Chapter 4. Renormalization.-
Chapter 5. The Three Ingredients for Convergence of Renormalization.
Chapter 6. The Collaboration of the Three Ingredients.
Chapter 7. Exponential Convergence.
Chapter 8. Geometry of Circle Diffeomorphisms.
Chapter 9. Non-Rigidity.
Chapter 10. The Renormalization Horseshoe.
Format: Hardback, 500 pages, height x width: 235x155 mm, 20 Illustrations, color; 30 Illustrations, black and white; Approx. 500 p. 50 illus., 20 illus. in color., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 503
Pub. Date: 08-Aug-2025
ISBN-13: 9783031932786
This book compiles carefully reviewed papers presented at the international conference "Approximation Theory and Special Functions - ATSF 2024," held in Ankara, Turkiye, from September 4-7, 2024. These contributions provide valuable insights into the latest developments at the intersection of approximation theory and special functions.
This work consists of two main parts: Approximation Theory and Special Functions. The Approximation Theory section focuses on topics such as classical approximation by operators, linear and nonlinear approximation, singular operators, fractional approximation, neural networks, numerical approximation, and interpolation. The Special Functions section deals with extremal polynomials, some newly introduced Appell polynomials, multivariate special polynomials, hypergeometric functions, generating functions, fixed point theory, potential theory, and their various applications.
This volume serves as an invaluable resource for a diverse audience, including researchers, practitioners in approximation theory and special functions, as well as graduate students attending advanced seminars.
ATSF is an international conference series organized to bring together researchers from all areas of Approximation Theory and Special Functions to discuss new ideas and new applications. This organization, which has been held seven times so far as mini-symposia, has grown gradually over the years. The 2024 edition, hosted by TOBB Economics and Technology University in Ankara, marks its eightieth iteration.
Interpolating projections in Frechet algebras.- Trigonometric Background
Multivariate Smooth Poisson-Cauchy Singular Integrals Approximation.-
Asymptotic and quantitative results of Neural Network operators that employ
wavelets.- Genuine Bernstein-Durrmeyer type operators preserving 1 and x^j
(II).- Korovkin-type approximation theorems for functions with the help of
Istatistical convergence.- Fractional Approximation of Time Separating
Stochastic Processes by Neural Networks of Compact Support.- Some Results of
Korovkin Type For Nonlinear Operators.- Approximation Properties of
Generalized Q-Favard-Sz´asz-Mirakjan Operators of Max-Product Kind.-
Riemann-Liouville Type Fractional Generalized $\lambda-$Bernstein-Kantorovich
Operators.- Parametric Extensions of a Certain Family of Bernstein-Type
Rational Functions.- Stability Analysis of a SAIR Epidemic Model with
Logistic Growth in Susceptible Compartment.- Numerical Solution and Effective
Error Estimation for a Mixed Problem for the Laplace Equation.- On Some
Comparison of Multi-step Multi-derivative Methods and Its Application to
Solve the Volterra Integro-Differential Equations.- Existence and Uniqueness
of strong Solution of the Time fractional integro differential equation with
integral boundary conditions.- The New Numerical Solutions of the
Atangana-Baleanu Fractional Benney Equation.- A New Dual-phase Hybrid
Variable Selection Method in High-Dimensional Data.- Certain New Integral
Formulas Involving the Generalized Multi-index Bessel Functions.- Lower
Bounds for Extremal Polynomials.- General Families of Cosine and Sine Appell
Polynomials.- Some properties of Frobenius-Sigmoid polynomials.- The
Appell-Fibonacci Polynomials.- On Bivariate Jacobi Konhauser Polynomials.-
The Multivariable-Multiparameter generalized Cesaro polynomials and
the generalized Lauricella functions.- The Difference Equation of Meijiers
G-function.- The generalized finite bivariate biorthogonal M - Jacobi
polynomials.- Probabilistic new type degenerate Bell polynomials of the
second kind associated with random variables.- Fuzzy Parameterized CR-Fuzzy
Soft Sets and Some Set Operations.- A Modified Similarity Measure for
Continuous Function Valued Intuitionistic Fuzzy Sets and An Application on
Classification.- Energy spectrum for Scarf-Grosche potential.- Some
Inequalities for Riesz Potential on Homogeneous Variable
Exponent Herz-Morrey-Hardy Spaces.- Fixed Point Results of Contractive
Mappings Under Simulation Function in Metric Spaces.- Completely Monotone
Invariance of Smoothing via Central Vector Lattice Differences.- Spectrum
Density Estimation of Sample Covariance Matrices with Correlated Entries.-
Modelling of Count Data in Circular Statistics.- Reconstruction of the North
Atlantic Double-gyre Circulation with Genetic Programming.- On Normal
Subgroups of General Linear Groups of Certain $C^*$-Algebras.
Format: Paperback / softback, 135 pages, height x width: 235x155 mm, 3 Illustrations, black and white; X, 135 p. 3 illus., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2371
Pub. Date: 30-Aug-2025
ISBN-13: 9783031943393
This book examines the symbiotic interplay between fully nonlinear elliptic partial differential equations and general potential theories of second order. Starting with a self-contained presentation of the classical theory of first and second order differentiability properties of convex functions, it collects a wealth of results on how to treat second order differentiability in a pointwise manner for merely semicontinuous functions. The exposition features an analysis of upper contact jets for semiconvex functions, a proof of the equivalence of two crucial, independently developed lemmas of Jensen (on the viscosity theory of PDEs) and Slodkowski (on pluripotential theory), and a detailed description of the semiconvex approximation of upper semicontinuous functions.
The foundations of general potential theories are covered, with a review of monotonicity and duality, and the basic tools in the viscosity theory of generalized subharmonics, culminating in an account of the monotonicity-duality method for proving comparison principles. The final section shows that the notion of semiconvexity extends naturally to manifolds. A complete treatment of important background results, such as Alexandrov’s theorem and a Lipschitz version of Sard’s lemma, is provided in two appendices.
The book is aimed at a wide audience, including professional mathematicians working in fully nonlinear PDEs, as well as master’s and doctoral students with an interest in mathematical analysis.
Part I. Semiconvex apparatus.
Chapter 1. Differentiability of convex functions.
Chapter 2. Semiconvex functions and upper contact jets.
Chapter 3. The lemmas of Jensen and Slodkowski.
Chapter 4. Semiconvex approximation of semicontinuous functions.-
Part II. General potential-theoretic analysis.-
Chapter 5. General potential theories.
Chapter 6. Duality and monotonicity in general potential theories.
Chapter 7. Basic tools in nonlinear potential theory.
Chapter 8. Semiconvex functions and subharmonics.
Chapter 9. Comparison principles.
Chapter 10. From Euclidean spaces to manifolds:
a brief note.
Format: Paperback / softback, 139 pages, height x width: 235x155 mm, XIX, 139 p., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2374
Pub. Date: 03-Aug-2025
ISBN-13: 9783031964053
This book highlights the use of non-compact analytic cycles in complex geometry. The main focus is on analytic families of cycles of finite type, in other words, cycles which have only finitely many irreducible components. It is shown how the space of all cycles of finite type in a given complex space, endowed with a weak analytic structure, can be used in many ways as the reduced complex space of all compact cycles in the given space. Several illustrative and enlightening examples are provided, as well as applications, giving life to the theory. The exposition includes a characterization of quasi-proper holomorphic maps which admit a geometric flattening, a proof of an existence theorem for meromorphic quotients with respect to a large class of analytic equivalence relations, and a generalization of the Stein factorization to a variety of holomorphic maps. In addition, a study is made of the behavior of analytic families of finite type cycles when they are restricted to Zariski open subsets and extended across analytic subsets.
Aimed at researchers and graduate students with an interest in complex or algebraic geometry, the book is adequately self-contained, the basic notions are explained and suitable references are given for auxiliary results that are used in the text.
Chapter 1. Semi-proper maps.
Chapter 2. Quasi-proper Maps.
Chapter 3. The space Cfn (M).
Chapter 4. f-Analytic Families of Cycles.
Chapter 5. Geometrically f-Flat Maps and Strongly Quasi-proper Maps.
Chapter 6. Applications.
Format: Paperback / softback, 230 pages, height x width: 235x155 mm, 13 Illustrations, color; 21 Illustrations, black and white; X, 230 p. 34 illus., 13 illus. in color., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2375
Pub. Date: 21-Aug-2025
ISBN-13: 9783031955914
This book provides a highly accessible approach to discrete surface theory, within the unifying frameworks of Moebius and Lie sphere geometries, from the perspective of transformation theory of surfaces rooted in integrable systems. It elucidates how the transformation theory for smooth surfaces can be used as a springboard for understanding the discretization process of certain types of surfaces, and it is aimed at high-level undergraduate students, graduate students and professional mathematicians alike. The reader will benefit from the detailed exploration of the transformation theory of surfaces, including Christoffel, Calapso and Darboux transformations of particular classes of surfaces, as well as becoming more familiar with integrable systems via zero curvature representation, including flat connections and conserved quantities, in both smooth and discrete settings.
Chapter 1. Introduction.
Chapter 2.Isothermic surfaces in Mobius geometry.
Chapter 3. From smooth to discrete via permutability.
Chapter 4. Discrete Isothermic surfaces.
Chapter 5. -surfaces in Lie sphere geometry.-
Chapter 6. Integrability of -surfaces via isothermicity.
Chapter 7. Discrete -surfaces.
Format: Paperback / softback, 205 pages, height x width: 235x155 mm, 55 Illustrations, black and white; X, 205 p. 55 illus., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2379
Pub. Date: 21-Aug-2025
ISBN-13: 9783031962080
This book provides a comprehensive introduction to the systematic theory of tensor products and tensor norms within the framework of operator spaces. The use of tensor products has significantly advanced functional analysis and other areas of mathematics and physics, and the field of operator spaces is no exception. Building on the theory of tensor products in Banach spaces, this work adapts the definitions and results to the operator space context. This approach goes beyond a mere translation of existing results. It introduces new insights, techniques, and hypotheses to address the many challenges of the non-commutative setting, revealing several notable differences to the classical theory. This text is expected to be a valuable resource for researchers and advanced students in functional analysis, operator theory, and related fields, offering new perspectives for both the mathematics and physics communities. By presenting several open problems, it also serves as a potential source for further research, particularly for those working in operator spaces or operator algebras.
Chapter 1. Preliminaries.
Chapter 2. Introduction to operator space tensor norms.
Chapter 3. Finite and cofinite hulls.
Chapter 4. The five basic lemmas.
Chapter 5. Dual operator space tensor norms.
Chapter 6. The completely bounded approximation property.
Chapter 7. Mapping ideals.-
Chapter 8. Maximal operator space mapping ideals.
Chapter 9. Minimal operator space mapping ideals.
Chapter 10. Completely projective/injective tensor norms.
Chapter 11. Injective/projective hulls and accessibility.-
Chapter 12. Natural operator space tensor norms.
Chapter 13. Conclusions and some open questions.