Edited by Barry Simon, Edited by Pavel Kurasov, Edited by Gunter Stolz, Edited by Malcolm Brown,
Edited by Ian Wood, Edited by Fritz Gesztesy, Edited by Ari Laptev

From Complex Analysis to Operator Theory:
A Panorama: In Memory of Sergey Naboko

Format: Paperback / softback, 698 pages, height x width: 235x155 mm,
1 Illustrations, black and white; XLVI, 698 p. 1 illus.,
Series: Operator Theory: Advances and Applications 291
Pub. Date: 24-Sep-2024
ISBN-13: 9783031311413

Description


This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Nabokofs scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Table of Contents

Part I On Some of Sergeys Works.- Working with Sergey Naboko on
Boundary Triples.- Operator-Valued NevanlinnaHerglotz Functions, Trace
Ideals, and Sergey Nabokos Contributions.- Mathematical Heritage of Sergey
Naboko: Functional Models of Non-Self-Adjoint Operators.- On Crossroads of
Spectral Theory with Sergey Naboko.- Sergey Nabokos Legacy on the Spectral
Theory of Jacobi Operators.- On theWork by Serguei Naboko on the Similarity
to Unitary and Selfadjoint Operators.- Part II Research Contributions.-
Functional Models of Symmetric and Selfadjoint Operators.- Schrodinger
Operators with -potentials Supported on Unbounded Lipschitz Hypersurfaces.-
Improved LiebThirring Type Inequalities for Non-selfadjoint Schrodinger
Operators.- Ballistic Transport in Periodic and Random Media.- On the
Spectral Theory of Systems of First Order Equations with Periodic
Distributional Coefficients.- Asymptotic Analysis of Operator Families and
Applications to Resonant Media.- On the Number and Sums of Eigenvalues of
Schrodinger-type Operators with Degenerate Kinetic Energy.- Gap Labelling for
Discrete One-Dimensional Ergodic Schrodinger Operators.- Degenerate Elliptic
Operators and Katos Inequality.- Generalized Indefinite Strings with Purely
Discrete Spectrum.- Soliton Asymptotics for the KdV Shock Problem of Low
Regularity.- Realizations of Meromorphic Functions of Bounded Type.- Spectral
Transition Model with the General Contact Interaction.- Weyls Law under
Minimal Assumptions.- WeylTitchmarsh M-Functions for -Periodic
SturmLiouville Operators in Terms of Greens Functions.- On Discrete Spectra
of BergmanToeplitz Operators with Harmonic Symbols.- One Dimensional
Discrete Schrodinger Operators with Resonant Embedded Eigenvalues.- On the
Invariance Principle for a Characteristic Function.- A Trace Formula and
Classical Solutions to the KdV Equation.- Semiclassical Analysis in the Limit
Circle Case.


Edmundo Capelas de Oliveira, Jose Em?lio Maiorino

Analytical Methods in Applied Mathematics

Hardback
Format: Hardback, 388 pages, height x width: 235x155 mm, 15 Illustrations, black and white; XIII, 388 p. 15 illus., 1 Hardback
Series: Problem Books in Mathematics
Pub. Date: 15-Nov-2024
ISBN-13: 9783031747939

Description

This book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering.

The book begins with an exploration of simple linear and nonlinear ordinary differential equations in Chapter 1, advancing through topics such as power series and the Frobenius method for solving differential equations in Chapter 2. In subsequent chapters, the discussion expands to include functions of complex variables, special functions constructed through the hypergeometric function, and series solutions including Fourier, Fourier-Bessel, and Fourier-Legendre series. Problems in integral transforms, Sturm-Liouville systems, Green's function, linear partial differential equations are also included. The work finishes with a special chapter on fractional calculus and practical applications of the topics presented.

With solved examples and step-by-step exercises, this book can be of value to undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well.

Table of Contents

Preface.- Ordinary Differential Equations.- Power Series and the Frobenius Method.- Laurent Series and Residues.- Special Functions.- Fourier, Fourier-Bessel and Fourier-Legendre Series.- Laplace and Fourier Transforms.- Sturm-Liouville Systems.- Partial Differential Equations.- Separation of Variables.- Fractional Calculus.- Applications.- Answers and Hints.- Index.

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Henrik Holm, Lars Winther Christensen, Hans-Bj?rn Foxby

Derived Category Methods in Commutative Algebra

Format: Hardback, 1119 pages, height x width: 235x155 mm, XXIII, 1119 p., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 05-Dec-2024
ISBN-13: 9783031774522

Description

Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendiecks Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand.

This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings.

The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject.

Table of Contents

1 Modules.- 2 Complexes.- 3 Categorical Constructions.- 4 Equivalences and Isomorphisms.- 5 Resolutions.- 6 The Derived Category.- 7 Derived Functors.- 8 Homological Dimensions.- 9 Gorenstein Homological Dimensions.- 10 Dualizing Complexes.- 11 Torsion and Completion.- 12 A Brief for Commutative Ring Theorists.- 13 Derived Torsion and Completion.- 14 Krull Dimension, Depth, and Width.- 15 Support Theories.- 16 Homological Invariants over Local Rings.- 17 Going Local.- 18 Dualities and Cohen-Macaulay Rings.- 19 Gorenstein Dimensions and Gorenstein Rings.- 20 Global Dimension and Regular Rings.- APPENDIX A: Acyclicity and Boundedness.- APPENDIX B: Minimality.- APPENDIX C: Structure of Injective Modules.- APPENDIX D: Projective Dimension of Flat Modules.- APPENDIX E: Triangulated Categories.

Hellmuth Stachel, Georg Glaeser, Boris Odehnal

Universe of Conics:
From the Ancient Greeks to 21st Century Developments Second Edition

Format: Hardback, 574 pages, height x width: 240x168 mm, X, 574 p., 1 Hardback
Pub. Date: 22-Jan-2025
ISBN-13: 9783662703052

Description

This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries.

With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics.

This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry.

Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.

Table of Contents

1 Introduction.- 2 Euclidean plane.- 3 Differential Geometry.- 4 Eucledian 3-space.- 5 Projective Geometry.- 6 Projective conics.- 7 Polarities and pencils.- 8 Affine Geometry.- 9 Special problems.- 10 Other geometries.- Index.

Stefan Muller-Stach

Richard Dedekind:
What Are and What Should the Numbers Be? Continuity and Irrational Numbers

Format: Hardback, 236 pages, height x width: 240x168 mm, 2 Illustrations, color; X, 236 p. 2 illus. in color., 1 Hardback
Series: Classic Texts in the Sciences
Pub. Date: 07-Dec-2024
ISBN-13: 9783662700563

Description

The two works titled "What Are and What Should the Numbers Be?" (1888) and "Continuity and Irrational Numbers" (1872) are Dedekind's contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind's achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today.

This volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind's pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann.

Researchers and students alike will find this work a valuable reference in the history of mathematics.

Table of Contents

Preface.-
1. Historical Introduction.-
2. Dedekinds Investigations into
the Concept of Number.-
3. Reprint of Dedekinds Books.-
4. Explanation of
the Texts in Todays Language.-
5. Reception History.-
6. Impact and
Positions of Research.- A Dedekinds Publications.- B The Letter to
Keferstein from February 27, 1890.- Bibliography.- Name and Subject Index.

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Edited by Brian Grajales, Edited by Duv?n Cardona

Analysis and PDE in Latin America:
ICMAM 2022

Format: Hardback, 160 pages, height x width: 235x155 mm, 1 Illustrations, color; IX, 160 p. 1 illus. in color., 1 Hardback
Series: Research Perspectives Ghent Analysis and PDE Center 10
Pub. Date: 30-Jan-2025
ISBN-13: 9783031732737

Description

This book presents the extended abstracts of the 2022 International Conference: Multidisciplinary Aspects in Mathematics and its applications (ICMAM) Latin America conference. The book presents the current state of the art in Analysis and PDEs in Latin America. Topics include: PDE models describing epidemics, population dynamics, climatological risks, oil prospection, impedance tomography in the detection of medical diseases, and abstract theory of PDEs. The extended abstracts presented in this book includes contributions by several renowned mathematicians in analysis and PDEs.

lknur Koca, Abdon Atangana

Fractional Differential and Integral Operators with Respect to a Function:
Theory Methods and Applications

Format: Hardback, 366 pages, height x width: 235x155 mm, 25 Illustrations, black and white; XII, 366 p. 25 illus., 1 Hardback
Series: Industrial and Applied Mathematics
Pub. Date: 09-Feb-2025
ISBN-13: 9789819799503

Description

This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals. The derivative, which measures a function's rate of change, is paired with its counterpart, the integral, used for calculating areas and volumes. Together, they form the backbone of differential and integral equations, widely applied in science, technology, and engineering. However, discrepancies between mathematical models and experimental data led to the development of extended integral forms, such as the Riemann?Stieltjes integral and fractional integrals, which integrate functions with respect to another function or involve convolutions with kernels. These extensions also gave rise to new types of derivatives, leading to fractional derivatives and integrals with respect to another function. While there has been limited theoretical exploration in recent years, this book aims to bridge that gap. It provides a comprehensive theoretical framework covering inequalities, nonlinear ordinary differential equations, numerical approximations, and their applications. Additionally, the book delves into the existence and uniqueness of solutions for nonlinear ordinary differential equations involving these advanced derivatives, as well as the development of numerical techniques for solving them.

Table of Contents

History of differential and integral calculus.-Global derivatives,
definitions and properties.- Integral operators, definitions and
properties.- Inequalities related to global fractional
derivatives.- Inequalities associated to Integrals.- Existence and Uniqueness
of IVP with global differentiation on via Picard iteration.- Existence and
uniqueness via Caratheodory approach.- Existence and uniqueness analysis of
nonlocal global differential equations with expectation
approach.- Chaplygins method for global differential equations.- Numerical
analysis of IVP with classical global derivative.-Numerical analysis of IVP
with Riemann-Liouville global derivative.- Numerical analysis of IVP with
Caputo-Fabrizio global derivative.- Numerical analysis of IVP with
Atangana-Baleanu global derivative.- Examples and applications of global
fractional differential equations.