Basic Analysis Of Regularized Series And Products
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Basic Analysis Of Regularized Series And Products
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Author : Jay Jorgenson
language : en
Publisher: Springer
Release Date : 2006-11-15
Basic Analysis Of Regularized Series And Products written by Jay Jorgenson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Analytic number theory and part of the spectral theory of operators (differential, pseudo-differential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of non-compact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and L-functions of number theory or representation theory and modular forms; to Selberg-like zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is self-contained (except for far-reaching examples), requiring only standard knowledge of analysis.
Basic Analysis Of Regularized Series And Products
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Author : Jay Jorgenson
language : en
Publisher:
Release Date : 2014-01-15
Basic Analysis Of Regularized Series And Products written by Jay Jorgenson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Number Theory Analysis And Geometry
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Author : Dorian Goldfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-21
Number Theory Analysis And Geometry written by Dorian Goldfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-21 with Mathematics categories.
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.
The Heat Kernel And Theta Inversion On Sl2 C
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Author : Jay Jorgenson
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-20
The Heat Kernel And Theta Inversion On Sl2 C written by Jay Jorgenson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-20 with Mathematics categories.
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform./
Heat Kernels And Analysis On Manifolds Graphs And Metric Spaces
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Author : Pascal Auscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Heat Kernels And Analysis On Manifolds Graphs And Metric Spaces written by Pascal Auscher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Elliptic operators categories.
This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.
Complex Analysis
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Complex Analysis written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than is found in other texts, and the resulting proofs often shed more light on the results than the standard proofs. While the first part is suitable for an introductory course at undergraduate level, the additional topics covered in the second part give the instructor of a gradute course a great deal of flexibility in structuring a more advanced course.
Collected Papers V
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-10-23
Collected Papers V written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-23 with Mathematics categories.
Serge Lang (1927-2005) was one of the top mathematicians of our time. He was born in Paris in 1927, and moved with his family to California, where he graduated from Beverly Hills High School in 1943. He subsequently graduated from California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951 before holding faculty positions at the University of Chicago and Columbia University (1955-1971). At the time of his death he was professor emeritus of Mathematics at Yale University. An excellent writer, Lang has made innumerable and invaluable contributions in diverse fields of mathematics. He was perhaps best known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was also a member of the Bourbaki group. He was honored with the Cole Prize by the American Mathematical Society as well as with the Prix Carrière by the French Academy of Sciences. These five volumes collect the majority of his research papers, which range over a variety of topics.
Collected Papers I
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-04-20
Collected Papers I written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-20 with Mathematics categories.
Serge Lang is not only one of the top mathematicians of our time, but also an excellent writer. He has made innumerable and invaluable contributions in diverse fields of mathematics and was honoured with the Cole Prize by the American Mathematical Society as well as with the Prix Carriere by the French Academy of Sciences. Here, 83 of his research papers are collected in four volumes, ranging over a variety of topics of interest to many readers.
Schr Dinger Operators Spectral Analysis And Number Theory
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Author : Sergio Albeverio
language : en
Publisher: Springer Nature
Release Date : 2021-06-03
Schr Dinger Operators Spectral Analysis And Number Theory written by Sergio Albeverio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-03 with Mathematics categories.
This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.
Fractal Geometry Complex Dimensions And Zeta Functions
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Author : Michel L. Lapidus
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-08
Fractal Geometry Complex Dimensions And Zeta Functions written by Michel L. Lapidus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-08 with Mathematics categories.
Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.