Edgar Krahn 1894-1961
Author: Ülo Lumiste
Publisher: IOS Press
Published: 1994
Total Pages: 212
ISBN-13: 9789051991680
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Edgar Krahn, a Centenary Volume
Author: J. Peetre
Publisher: IOS Press
Published: 1994-08
Total Pages: 196
ISBN-13: 9789051991680
DOWNLOAD EBOOKEdgar Krahn was one of the two authors of the celebrated FaberKrahn inequality connected with the Rayleigh conjecture and who was one of the first to consider isoperimetric problems in the multidimensional case. This volume commenmorates his 100th birthday and surveys the major implicaions of his work in this century.
Analytic and Geometric Inequalities and Applications
Author: Themistocles RASSIAS
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 377
ISBN-13: 9401145776
DOWNLOAD EBOOKAnalytic and Geometric Inequalities and Applications is devoted to recent advances in a variety of inequalities of Mathematical Analysis and Geo metry. Subjects dealt with in this volume include: Fractional order inequalities of Hardy type, differential and integral inequalities with initial time differ ence, multi-dimensional integral inequalities, Opial type inequalities, Gruss' inequality, Furuta inequality, Laguerre-Samuelson inequality with extensions and applications in statistics and matrix theory, distortion inequalities for ana lytic and univalent functions associated with certain fractional calculus and other linear operators, problem of infimum in the positive cone, alpha-quasi convex functions defined by convolution with incomplete beta functions, Chebyshev polynomials with integer coefficients, extremal problems for poly nomials, Bernstein's inequality and Gauss-Lucas theorem, numerical radii of some companion matrices and bounds for the zeros of polynomials, degree of convergence for a class of linear operators, open problems on eigenvalues of the Laplacian, fourth order obstacle boundary value problems, bounds on entropy measures for mixed populations as well as controlling the velocity of Brownian motion by its terminal value. A wealth of applications of the above is also included. We wish to express our appreciation to the distinguished mathematicians who contributed to this volume. Finally, it is our pleasure to acknowledge the fine cooperation and assistance provided by the staff of Kluwer Academic Publishers. June 1999 Themistocles M. Rassias Hari M.
Topics in Spectral Geometry
Author: Michael Levitin
Publisher: American Mathematical Society
Published: 2023-11-30
Total Pages: 346
ISBN-13: 1470475251
DOWNLOAD EBOOKIt is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.
Complex Quantum Systems: Analysis Of Large Coulomb Systems
Author: Heinz Siedentop
Publisher: World Scientific
Published: 2013-05-20
Total Pages: 303
ISBN-13: 9814460168
DOWNLOAD EBOOKThis volume is based on lectures given during the program “Complex Quantum Systems” held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many-body methods originating from quantum information, and — the most complex — semirelativistic quantum electrodynamics.These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.
Spectral Analysis of Quantum Hamiltonians
Author: Rafael Benguria
Publisher: Springer Science & Business Media
Published: 2012-06-30
Total Pages: 341
ISBN-13: 3034804148
DOWNLOAD EBOOKThis volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.
Mathematical Constants
Author: Steven R. Finch
Publisher: Cambridge University Press
Published: 2003-08-18
Total Pages: 634
ISBN-13: 9780521818056
DOWNLOAD EBOOKSteven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Spectral Theory and Geometry
Author: E. Brian Davies
Publisher: Cambridge University Press
Published: 1999-09-30
Total Pages: 344
ISBN-13: 0521777496
DOWNLOAD EBOOKAuthoritative lectures from world experts on spectral theory and geometry.
A Course in the Calculus of Variations
Author: Filippo Santambrogio
Publisher: Springer Nature
Published: 2024-01-18
Total Pages: 354
ISBN-13: 3031450361
DOWNLOAD EBOOKThis book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.
Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities
Author: Rupert L. Frank
Publisher: Cambridge University Press
Published: 2022-11-17
Total Pages: 524
ISBN-13: 1009218441
DOWNLOAD EBOOKThe analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample amount of background material on the spectral theory of linear operators in Hilbert spaces and on Sobolev space theory. Of particular interest is a family of inequalities by Lieb and Thirring on eigenvalues of Schrödinger operators, which they used in their proof of stability of matter. The final part of this book is devoted to the active research on sharp constants in these inequalities and contains state-of-the-art results, serving as a reference for experts and as a starting point for further research.
