The Method Of Layer Potentials For The Heat Equation In Time Varying Domains

Author : John L. Lewis
Publisher : American Mathematical Soc.
ISBN 13 : 0821803603
Total Pages : 170 pages
Book Rating : 4.08/5 ( download)

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Download or read book The Method of Layer Potentials for the Heat Equation in Time-Varying Domains written by John L. Lewis and published by American Mathematical Soc.. This book was released on 1995 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir consists of three papers in which we develop the method of layer potentials for the heat equation in time-varying domains. In Chapter I we show certain singular integral operators on [italic]L[superscript italic]p are bounded. in Chapter II, we develop a modification of the David buildup scheme to obtain [italic]L[superscript italic]p boundedness of the double layer heat potential on the boundary of our domains. In Chapter III, we use the results of the first two chapters to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure.

Author : Stefania A. M. Marcantognini
Publisher : American Mathematical Soc.
ISBN 13 : 0821803042
Total Pages : 528 pages
Book Rating : 4.42/5 ( download)

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Download or read book Harmonic Analysis and Operator Theory written by Stefania A. M. Marcantognini and published by American Mathematical Soc.. This book was released on 1995 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection covers a broad spectrum of topics, including: wavelet analysis, Haenkel operators, multimeasure theory, the boundary behavior of the Bergman kernel, interpolation theory, and Cotlar's Lemma on almost orthogonality in the context of L[superscript p] spaces and more...

Author : Jose Garcia-Cuerva
Publisher : CRC Press
ISBN 13 : 135108903X
Total Pages : 335 pages
Book Rating : 4.36/5 ( download)

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Download or read book Fourier Analysis and Partial Differential Equations written by Jose Garcia-Cuerva and published by CRC Press. This book was released on 2018-01-18 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Analysis and Partial Differential Equations presents the proceedings of the conference held at Miraflores de la Sierra in June 1992. These conferences are held periodically to assess new developments and results in the field. The proceedings are divided into two parts. Four mini-courses present a rich and actual piece of mathematics assuming minimal background from the audience and reaching the frontiers of present-day research. Twenty lectures cover a wide range of data in the fields of Fourier analysis and PDE. This book, representing the fourth conference in the series, is dedicated to the late mathematician Antoni Zygmund, who founded the Chicago School of Fourier Analysis, which had a notable influence in the development of the field and significantly contributed to the flourishing of Fourier analysis in Spain.

Author : Ole H. Hald
Publisher : American Mathematical Soc.
ISBN 13 : 0821804863
Total Pages : 162 pages
Book Rating : 4.65/5 ( download)

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Download or read book Inverse Nodal Problems: Finding the Potential from Nodal Lines written by Ole H. Hald and published by American Mathematical Soc.. This book was released on 1996 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.

Author : Dihua Jiang
Publisher : American Mathematical Soc.
ISBN 13 : 0821804766
Total Pages : 210 pages
Book Rating : 4.66/5 ( download)

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Download or read book Degree 16 Standard L-function of $GSp(2) \times GSp(2)$ written by Dihua Jiang and published by American Mathematical Soc.. This book was released on 1996 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic L-functions, introduced by Robert Langlands in the 1960s, are natural extensions of such classical L-functions as the Riemann zeta function, Hecke L-functions, etc. They form an important part of the Langlands Program, which seeks to establish connections among number theory, representation theory, and geometry. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic groups, and the relevant residue representations.

Author : Tai-Ping Liu
Publisher : American Mathematical Soc.
ISBN 13 : 0821805452
Total Pages : 135 pages
Book Rating : 4.59/5 ( download)

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Download or read book Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 1997 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-asymptotic behavior of the solutions. This yields optimal estimates in the integral norms. For most physical models, the viscosity matrix is not positive definite and the system is hyperbolic-parabolic, and not uniformly parabolic. This implies that the Green's function may contain Dirac [lowercase Greek]Delta-functions. When the corresponding inviscid system is non-strictly hyperbolic, the time-asymptotic state contains generalized Burgers solutions. These are illustrated by applying our general theory to the compressible Navier-Stokes equations and the equations of magnetohydrodynamics.

Author : N. A. Watson
Publisher : American Mathematical Soc.
ISBN 13 : 0821849980
Total Pages : 282 pages
Book Rating : 4.89/5 ( download)

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Download or read book Introduction to Heat Potential Theory written by N. A. Watson and published by American Mathematical Soc.. This book was released on 2012 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to be devoted entirely to the potential theory of the heat equation, and thus deals with time dependent potential theory. Its purpose is to give a logical, mathematically precise introduction to a subject where previously many proofs were not written in detail, due to their similarity with those of the potential theory of Laplace's equation. The approach to subtemperatures is a recent one, based on the Poisson integral representation of temperatures on a circular cylinder. Characterizations of subtemperatures in terms of heat balls and modified heat balls are proved, and thermal capacity is studied in detail. The generalized Dirichlet problem on arbitrary open sets is given a treatment that reflects its distinctive nature for an equation of parabolic type. Also included is some new material on caloric measure for arbitrary open sets. Each chapter concludes with bibliographical notes and open questions. The reader should have a good background in the calculus of functions of several variables, in the limiting processes and inequalities of analysis, in measure theory, and in general topology for Chapter 9.

Author : Stéphane Jaffard
Publisher : American Mathematical Soc.
ISBN 13 : 0821804758
Total Pages : 127 pages
Book Rating : 4.59/5 ( download)

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Download or read book Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions written by Stéphane Jaffard and published by American Mathematical Soc.. This book was released on 1996 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate several topics related to the local behavior of functions: pointwise Hölder regularity, local scaling invariance and very oscillatory "chirp-like" behaviors. Our main tool is to relate these notions to two-microlocal conditions which are defined either on the Littlewood-Paley decomposition or on the wavelet transform. We give characterizations and the main properties of these two-microlocal spaces and we give several applications, such as bounds on the dimension of the set of Hölder singularities of a function, Sobolev regularity of trace functions, and chirp expansions of specific functions.

Author : Valentina Barucci
Publisher : American Mathematical Soc.
ISBN 13 : 0821805444
Total Pages : 95 pages
Book Rating : 4.42/5 ( download)

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Download or read book Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains written by Valentina Barucci and published by American Mathematical Soc.. This book was released on 1997 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Chapter I, various (numerical) semigroup-theoretic concepts and constructions are introduced and characterized. Applications in Chapter II are made to the study of Noetherian local one-dimensional analytically irreducible integral domains, especially for the Gorenstein, maximal embedding dimension, and Arf cases, as well as to the so-called Kunz case, a pervasive kind of domain of Cohen-Macaulay type 2.

Author : Bruce Normansell Allison
Publisher : American Mathematical Soc.
ISBN 13 : 0821805940
Total Pages : 138 pages
Book Rating : 4.47/5 ( download)

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Download or read book Extended Affine Lie Algebras and Their Root Systems written by Bruce Normansell Allison and published by American Mathematical Soc.. This book was released on 1997 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is about extended affine Lie algebras (EALA's) and their root systems. EALA's were introduced by Høegh-Krohn and Torresani under the name irreducible quasi-simple Lie algebras. The major objective is to develop enough theory to provide a firm foundation for further study of EALA's. The first chapter of the paper is devoted to establishing some basic structure theory. It includes a proof of the fact that, as conjectured by Kac, the invariant symmetric bilinear form on an EALA can be scaled so that its restriction to the real span of the root system is positive semi-definite. The second chapter studies extended affine root systems (EARS) which are an axiomatized version of the root systems arising from EALA's. The concept of a semilattice is used to give a complete description of EARS. In the final chapter, a number of new examples of extended affine Lie algebras are given. The concluding appendix contains an axiomatic characterization of the nonisotropic roots in an EARS in a more general context than the one used in the rest of the paper.