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The Heat Kernel and Theta Inversion on SL2(C)

2009-02-20 Mathematics
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Release : 2009-02-20
Genre : Mathematics
Kind : eBook
Book Rating : 329/5 ( reviews)

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Book Synopsis The Heat Kernel and Theta Inversion on SL2(C) by : Jay Jorgenson

Download or read book The Heat Kernel and Theta Inversion on SL2(C) written by Jay Jorgenson. This book was released on 2009-02-20. Available in PDF, EPUB and Kindle. Book excerpt: 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

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 839/5 ( reviews)

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Book Synopsis Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by : Pascal Auscher

Download or read book Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces written by Pascal Auscher. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Number Theory, Analysis and Geometry

2011-12-21 Mathematics
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Release : 2011-12-21
Genre : Mathematics
Kind : eBook
Book Rating : 609/5 ( reviews)

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Book Synopsis Number Theory, Analysis and Geometry by : Dorian Goldfeld

Download or read book Number Theory, Analysis and Geometry written by Dorian Goldfeld. This book was released on 2011-12-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Heat Eisenstein Series on $\mathrm {SL}_n(C)$

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 444/5 ( reviews)

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Book Synopsis Heat Eisenstein Series on $\mathrm {SL}_n(C)$ by : Jay Jorgenson

Download or read book Heat Eisenstein Series on $\mathrm {SL}_n(C)$ written by Jay Jorgenson. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this Memoir is to define and study multi-variable Eisenstein series attached to heat kernels. Fundamental properties of heat Eisenstein series are proved, and conjectural behavior, including their role in spectral expansions, are stated.

The Ubiquitous Heat Kernel

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 986/5 ( reviews)

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Book Synopsis The Ubiquitous Heat Kernel by : Jay Jorgenson

Download or read book The Ubiquitous Heat Kernel written by Jay Jorgenson. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.

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