Theory and Applications of Differentiable Functions of Several Variables
Theory and Applications of Differentiable Functions of Several Variables

Author:

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 276

ISBN-13: 9780821802762

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This book explores various topical trends in the theory of differentiable functions of several real variables and its applications. Among the subjects covered are: imbedding of various spaces of differentiable functions defined on sets in Euclidean space, on a sphere, and in a polydisc; approximation of functions; estimates for the norms of various integral operators in weighted space; conditions for stabilization of a function to a polynomial; sufficient conditions for multipliers; construction of unconditional bases in anisotropic spaces; existence of entire solutions for quasilinear equations; and establishment of an asymptotic formula for the kernels of powers of the resolvent of elliptic operators.

Theory and Applications of Differentiable Functions of Several Variables
Theory and Applications of Differentiable Functions of Several Variables

Author: Lev Dmitrievich Kudri︠a︡vt︠s︡ev

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 300

ISBN-13: 9780821803387

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This book is dedicated to Sergei Mikhailovich Nikol'skii on the occasion of his eighty-fifth birthday. The collection contains new results on the following topics: approximation of functions, imbedding theory, interpolation of function spaces, convergence of series in trigonometric and general orthogonal systems, quasilinear elliptic problems, spectral theory of nonselfadjoint operators, asymptotic properties of pseudodifferential operators, and methods of approximate solution of Laplace's equation.

Theory and Applications of Differentiable Functions of Several Variables
Theory and Applications of Differentiable Functions of Several Variables

Author:

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 276

ISBN-13: 9780821831526

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This collection is the 14th in an ongoing series on differentiable functions of several variables, presenting recent contributions to a line of research begun by Sobolev in 1950. The papers study various spaces of differentiable functions of several real variables in Euclidean space, their imbeddings, equivalent normings, weighted estimates of derivatives, and traces on sets. Several questions of approximation in function spaces on the line, on a hyperboloid, and on Lobachevsky space are studied. Investigations of bilinear approximations are applied to estimates of the singular numbers of integral operators and widths. The authors also examine the asymptotics of the spectrum of elliptic systems, as well as the Dirichlet variational problem for a degenerate elliptic operator. Finally, a block method of solving Laplace's equation for nonanalytic boundary conditions is developed.