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Paley-Wiener Theorems for a p-Adic Spherical Variety

Paley-Wiener Theorems for a p-Adic Spherical Variety PDF Author: Patrick Delorme
Publisher: American Mathematical Soc.
ISBN: 147044402X
Category : Education
Languages : en
Pages : 102

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Book Description
Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].

Paley-Wiener Theorems for a p-Adic Spherical Variety

Paley-Wiener Theorems for a p-Adic Spherical Variety PDF Author: Patrick Delorme
Publisher: American Mathematical Soc.
ISBN: 147044402X
Category : Education
Languages : en
Pages : 102

Get Book Here

Book Description
Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].

Representation Theory, Number Theory, and Invariant Theory

Representation Theory, Number Theory, and Invariant Theory PDF Author: Jim Cogdell
Publisher: Birkhäuser
ISBN: 3319597280
Category : Mathematics
Languages : en
Pages : 630

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Book Description
This book contains selected papers based on talks given at the "Representation Theory, Number Theory, and Invariant Theory" conference held at Yale University from June 1 to June 5, 2015. The meeting and this resulting volume are in honor of Professor Roger Howe, on the occasion of his 70th birthday, whose work and insights have been deeply influential in the development of these fields. The speakers who contributed to this work include Roger Howe's doctoral students, Roger Howe himself, and other world renowned mathematicians. Topics covered include automorphic forms, invariant theory, representation theory of reductive groups over local fields, and related subjects.

Arthur Packets for $p$-adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples

Arthur Packets for $p$-adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples PDF Author: Clifton Cunningham
Publisher: American Mathematical Society
ISBN: 1470451174
Category : Mathematics
Languages : en
Pages : 232

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Book Description
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Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs

Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs PDF Author: Stefan Geiss
Publisher: American Mathematical Society
ISBN: 1470449358
Category : Mathematics
Languages : en
Pages : 112

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Instability, Index Theorem, and Exponential Trichotomy for Linear Hamiltonian PDEs

Instability, Index Theorem, and Exponential Trichotomy for Linear Hamiltonian PDEs PDF Author: Zhiwu Lin
Publisher: American Mathematical Society
ISBN: 1470450445
Category : Mathematics
Languages : en
Pages : 136

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Hamiltonian Perturbation Theory for Ultra-Differentiable Functions

Hamiltonian Perturbation Theory for Ultra-Differentiable Functions PDF Author: Abed Bounemoura
Publisher: American Mathematical Soc.
ISBN: 147044691X
Category : Education
Languages : en
Pages : 89

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Book Description
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency satisfies some arithmetic condition which we call BRM, and which generalizes the Bruno-R¨ussmann condition; and Nekhoroshev’s theorem, where the stability time depends on the ultra-differentiable class of the pertubation, through the same sequence M. Our proof uses periodic averaging, while a substitute for the analyticity width allows us to bypass analytic smoothing. We also prove converse statements on the destruction of invariant tori and on the existence of diffusing orbits with ultra-differentiable perturbations, by respectively mimicking a construction of Bessi (in the analytic category) and MarcoSauzin (in the Gevrey non-analytic category). When the perturbation space satisfies some additional condition (we then call it matching), we manage to narrow the gap between stability hypotheses (e.g. the BRM condition) and instability hypotheses, thus circumbscribing the stability threshold. The formulas relating the growth M of derivatives of the perturbation on the one hand, and the arithmetics of robust frequencies or the stability time on the other hand, bring light to the competition between stability properties of nearly integrable systems and the distance to integrability. Due to our method of proof using width of regularity as a regularizing parameter, these formulas are closer to optimal as the the regularity tends to analyticity

Elliptic Theory for Sets with Higher Co-Dimensional Boundaries

Elliptic Theory for Sets with Higher Co-Dimensional Boundaries PDF Author: Guy David
Publisher: American Mathematical Society
ISBN: 1470450437
Category : Mathematics
Languages : en
Pages : 123

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Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry

Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry PDF Author: Stuart Margolis
Publisher: American Mathematical Society
ISBN: 1470450429
Category : Mathematics
Languages : en
Pages : 135

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Uniqueness of Fat-Tailed Self-Similar Profiles to Smoluchowski?s Coagulation Equation for a Perturbation of the Constant Kernel

Uniqueness of Fat-Tailed Self-Similar Profiles to Smoluchowski?s Coagulation Equation for a Perturbation of the Constant Kernel PDF Author: Sebastian Throm
Publisher: American Mathematical Society
ISBN: 147044786X
Category : Mathematics
Languages : en
Pages : 106

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The Yang-Mills Heat Equation with Finite Action in Three Dimensions

The Yang-Mills Heat Equation with Finite Action in Three Dimensions PDF Author: Leonard Gross
Publisher: American Mathematical Society
ISBN: 1470450534
Category : Mathematics
Languages : en
Pages : 111

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