Higher Order Time Asymptotics Of Fast Diffusion In Euclidean Space A Dynamical Systems Approach

Higher Order Time Asymptotics Of Fast Diffusion In Euclidean Space A Dynamical Systems Approach Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Higher Order Time Asymptotics Of Fast Diffusion In Euclidean Space A Dynamical Systems Approach book. This book definitely worth reading, it is an incredibly well-written.

Higher-order Time Asymptotics of Fast Diffusion in Euclidean Space

Jochen Denzler,Herbert Koch,Robert J. McCann,American Mathematical Society
Higher order Time Asymptotics of Fast Diffusion in Euclidean Space Book PDF

Author : Jochen Denzler,Herbert Koch,Robert J. McCann,American Mathematical Society
Publisher : Unknown
Page : 81 pages
File Size : 44,8 Mb
Release : 2014
Category : Electronic books
ISBN : 1470420287

Get Book

Higher-order Time Asymptotics of Fast Diffusion in Euclidean Space by Jochen Denzler,Herbert Koch,Robert J. McCann,American Mathematical Society Pdf

This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on R [superscript]n to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. We provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.

Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach

Jochen Denzler,Herbert Koch, Robert J. McCann
Higher Order Time Asymptotics of Fast Diffusion in Euclidean Space A Dynamical Systems Approach Book PDF

Author : Jochen Denzler,Herbert Koch, Robert J. McCann
Publisher : American Mathematical Soc.
Page : 81 pages
File Size : 51,5 Mb
Release : 2015-02-06
Category : Mathematics
ISBN : 9781470414085

Get Book

Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach by Jochen Denzler,Herbert Koch, Robert J. McCann Pdf

This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.

Higher Moments of Banach Space Valued Random Variables

Svante Janson,Sten Kaijser
Higher Moments of Banach Space Valued Random Variables Book PDF

Author : Svante Janson,Sten Kaijser
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 42,5 Mb
Release : 2015-10-27
Category : Banach spaces
ISBN : 9781470414658

Get Book

Higher Moments of Banach Space Valued Random Variables by Svante Janson,Sten Kaijser Pdf

The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

On the Differential Structure of Metric Measure Spaces and Applications

Nicola Gigli
On the Differential Structure of Metric Measure Spaces and Applications Book PDF

Author : Nicola Gigli
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 41,8 Mb
Release : 2015-06-26
Category : Differential calculus
ISBN : 9781470414207

Get Book

On the Differential Structure of Metric Measure Spaces and Applications by Nicola Gigli Pdf

The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like , where is a function and is a measure. (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail.

Hitting Probabilities for Nonlinear Systems of Stochastic Waves

Robert C. Dalang,Marta Sanz-Solé
Hitting Probabilities for Nonlinear Systems of Stochastic Waves Book PDF

Author : Robert C. Dalang,Marta Sanz-Solé
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 43,8 Mb
Release : 2015-08-21
Category : Hausdorff measures
ISBN : 9781470414238

Get Book

Hitting Probabilities for Nonlinear Systems of Stochastic Waves by Robert C. Dalang,Marta Sanz-Solé Pdf

The authors consider a d-dimensional random field u={u(t,x)} that solves a non-linear system of stochastic wave equations in spatial dimensions k∈{1,2,3}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent β. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of Rd, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when d(2−β)>2(k+1), points are polar for u. Conversely, in low dimensions d, points are not polar. There is, however, an interval in which the question of polarity of points remains open.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Gaëtan Chenevier, David A. Renard
Level One Algebraic Cusp Forms of Classical Groups of Small Rank Book PDF

Author : Gaëtan Chenevier, David A. Renard
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 53,8 Mb
Release : 2015-08-21
Category : Cusp forms (Mathematics)
ISBN : 9781470410940

Get Book

Level One Algebraic Cusp Forms of Classical Groups of Small Rank by Gaëtan Chenevier, David A. Renard Pdf

The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.

Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem

Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni
Geometric Complexity Theory IV Nonstandard Quantum Group for the Kronecker Problem Book PDF

Author : Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 43,8 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410117

Get Book

Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem by Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni Pdf

The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.

Deformation Theory and Local-Global Compatibility of Langlands Correspondences

Martin Luu
Deformation Theory and Local Global Compatibility of Langlands Correspondences Book PDF

Author : Martin Luu
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 45,5 Mb
Release : 2015-10-27
Category : Automorphic forms
ISBN : 9781470414221

Get Book

Deformation Theory and Local-Global Compatibility of Langlands Correspondences by Martin Luu Pdf

The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.

On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation

M. Escobedo,J. J. L. Velázquez
On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation Book PDF

Author : M. Escobedo,J. J. L. Velázquez
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 46,7 Mb
Release : 2015-10-27
Category : SCIENCE
ISBN : 9781470414344

Get Book

On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation by M. Escobedo,J. J. L. Velázquez Pdf

The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4

Bob Oliver
Reduced Fusion Systems over 2 Groups of Sectional Rank at Most 4 Book PDF

Author : Bob Oliver
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 45,5 Mb
Release : 2016-01-25
Category : Algebraic topology
ISBN : 9781470415488

Get Book

Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 by Bob Oliver Pdf

The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk

A. Rod Gover,Emanuele Latini,Andrew Waldron
Poincare Einstein Holography for Forms via Conformal Geometry in the Bulk Book PDF

Author : A. Rod Gover,Emanuele Latini,Andrew Waldron
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 49,5 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410926

Get Book

Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk by A. Rod Gover,Emanuele Latini,Andrew Waldron Pdf

The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.

Endoscopic Classification of Representations of Quasi-Split Unitary Groups

Chung Pang Mok
Endoscopic Classification of Representations of Quasi Split Unitary Groups Book PDF

Author : Chung Pang Mok
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 54,5 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410414

Get Book

Endoscopic Classification of Representations of Quasi-Split Unitary Groups by Chung Pang Mok Pdf

In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.

Locally AH-Algebras

Huaxin Lin
Locally AH Algebras Book PDF

Author : Huaxin Lin
Publisher : American Mathematical Soc.
Page : 109 pages
File Size : 50,6 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470414665

Get Book

Locally AH-Algebras by Huaxin Lin Pdf

A unital separable -algebra, is said to be locally AH with no dimension growth if there is an integer satisfying the following: for any and any compact subset there is a unital -subalgebra, of with the form , where is a compact metric space with covering dimension no more than and is a projection, such that The authors prove that the class of unital separable simple -algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple -algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.

Spectral Means of Central Values of Automorphic L-Functions for GL(2)

Masao Tsuzuki
Spectral Means of Central Values of Automorphic L Functions for GL 2 Book PDF

Author : Masao Tsuzuki
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 41,7 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410193

Get Book

Spectral Means of Central Values of Automorphic L-Functions for GL(2) by Masao Tsuzuki Pdf

Starting with Green's functions on adele points of considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central -values attached to cuspidal waveforms with square-free level.

Classification of $E_0$-Semigroups by Product Systems

Michael Skeide
Classification of E 0 Semigroups by Product Systems Book PDF

Author : Michael Skeide
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 54,9 Mb
Release : 2016-03-10
Category : Endomorphisms (Group theory)
ISBN : 9781470417383

Get Book

Classification of $E_0$-Semigroups by Product Systems by Michael Skeide Pdf

In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.