Higher Order Time Asymptotics Of Fast Diffusion In Euclidean Space

Higher Order Time Asymptotics Of Fast Diffusion In Euclidean Space 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 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 : 41,6 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 : 52,5 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.

Mathematical Congress of the Americas

Jimmy Petean
Mathematical Congress of the Americas Book PDF

Author : Jimmy Petean
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 43,7 Mb
Release : 2016-01-25
Category : Mathematics
ISBN : 9781470423100

Get Book

Mathematical Congress of the Americas by Jimmy Petean Pdf

This volume contains the proceedings of the First Mathematical Congress of the Americas, held from August 5-9, 2013, in Guanajuato, México. With the participation of close to 1,000 researchers from more than 40 countries, the meeting set a benchmark for mathematics in the two continents. The papers, written by some of the plenary and invited speakers, as well as winners of MCA awards, cover new developments in classic topics such as Hopf fibrations, minimal surfaces, and Markov processes, and provide recent insights on combinatorics and geometry, isospectral spherical space forms, homogenization on manifolds, and Lagrangian cobordism, as well as applications to physics and biology.

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 : 44,7 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.

Classes of Polish Spaces Under Effective Borel Isomorphism

Vassilios Gregoriades
Classes of Polish Spaces Under Effective Borel Isomorphism Book PDF

Author : Vassilios Gregoriades
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 51,7 Mb
Release : 2016-03-10
Category : Isomorphisms (Mathematics)
ISBN : 9781470415631

Get Book

Classes of Polish Spaces Under Effective Borel Isomorphism by Vassilios Gregoriades Pdf

The author studies the equivalence classes under Δ11 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of Δ11-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.

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 : 52,7 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.

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 : 49,8 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.

Moduli of Double EPW-Sextics

Kieran G. O'Grady
Moduli of Double EPW Sextics Book PDF

Author : Kieran G. O'Grady
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 54,6 Mb
Release : 2016-03-10
Category : Equations, Sextic
ISBN : 9781470416966

Get Book

Moduli of Double EPW-Sextics by Kieran G. O'Grady Pdf

The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.

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 : 47,6 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.

The Fourier Transform for Certain HyperKahler Fourfolds

Mingmin Shen,Charles Vial
The Fourier Transform for Certain HyperKahler Fourfolds Book PDF

Author : Mingmin Shen,Charles Vial
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 51,9 Mb
Release : 2016-03-10
Category : Fourier transformations
ISBN : 9781470417406

Get Book

The Fourier Transform for Certain HyperKahler Fourfolds by Mingmin Shen,Charles Vial Pdf

Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle representing the Beauville-Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

Volker Bach,Jean-Bernard Bru
Diagonalizing Quadratic Bosonic Operators by Non Autonomous Flow Equations Book PDF

Author : Volker Bach,Jean-Bernard Bru
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 40,8 Mb
Release : 2016-03-10
Category : Hamiltonian operator
ISBN : 9781470417055

Get Book

Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations by Volker Bach,Jean-Bernard Bru Pdf

The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

Period Functions for Maass Wave Forms and Cohomology

R. Bruggeman,J. Lewis,D. Zagier
Period Functions for Maass Wave Forms and Cohomology Book PDF

Author : R. Bruggeman,J. Lewis,D. Zagier
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 45,8 Mb
Release : 2015-08-21
Category : Algebraic topology
ISBN : 9781470414078

Get Book

Period Functions for Maass Wave Forms and Cohomology by R. Bruggeman,J. Lewis,D. Zagier Pdf

The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.

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 : 40,8 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.

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 : 41,8 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 Quantization for Actions of Kahlerian Lie Groups

Pierre Bieliavsky,Victor Gayral
Deformation Quantization for Actions of Kahlerian Lie Groups Book PDF

Author : Pierre Bieliavsky,Victor Gayral
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 52,7 Mb
Release : 2015-06-26
Category : Kählerian structures
ISBN : 9781470414917

Get Book

Deformation Quantization for Actions of Kahlerian Lie Groups by Pierre Bieliavsky,Victor Gayral Pdf

Let B be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action of B on a Fréchet algebra . Denote by the associated Fréchet algebra of smooth vectors for this action. In the Abelian case BR and isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures R on . When is a -algebra, every deformed Fréchet algebra admits a compatible pre- -structure, hence yielding a deformation theory at the level of -algebras too. In this memoir, the authors prove both analogous statements for general negatively curved Kählerian groups. The construction relies on the one hand on combining a non-Abelian version of oscillatory integral on tempered Lie groups with geom,etrical objects coming from invariant WKB-quantization of solvable symplectic symmetric spaces, and, on the second hand, in establishing a non-Abelian version of the Calderón-Vaillancourt Theorem. In particular, the authors give an oscillating kernel formula for WKB-star products on symplectic symmetric spaces that fiber over an exponential Lie group.