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OverviewThis monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard. The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation. The second part deals with a number of problems of analytic continuations of analytic and harmonic functions. The third part is concerned with the investigation of the so-called inverse problems for differential equations in which it is required to determine a dif ferential equation from a certain family of its solutions. Novosibirsk June, 1967 M. M. LAVRENTIEV Table of Contents Chapter I Formu1ation of some Improperly Posed Problems of Mathematic:al Physics § 1 Improperly Posed Problems in Metric Spaces. . . . . . . . . § 2 A Probability Approach to Improperly Posed Problems. . . 8 Chapter II Analytic Continuation § 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 § 2 The Cauchy Problem for the Laplace Equation . . . . . . . 18 § 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity. . . . . . . . . . . . . 22 § 4 Analytic Continuation of a Function of Two Real Variables 32 § 5 Analytic Continuation of Harmonic Functions from a Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 § 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter III Inverse Problems for Differential Equations § 1 The Inverse Problem for a Newtonian Potential . . . . . . . Full Product DetailsAuthor: Michail M. Lavrentiev , R.J. Sacker , R.J. SackerPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1967 Volume: 11 Dimensions: Width: 15.50cm , Height: 0.40cm , Length: 23.50cm Weight: 0.159kg ISBN: 9783642882128ISBN 10: 3642882129 Pages: 76 Publication Date: 19 April 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsI Formulation of some Improperly Posed Problems of Mathematical Physics.- § 1 Improperly Posed Problems in Metric Spaces.- § 2 A Probability Approach to Improperly Posed Problems.- II Analytic Continuation.- § 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity.- § 2 The Cauchy Problem for the Laplace Equation.- § 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity.- § 4 Analytic Continuation of a Function of Two Real Variables.- § 5 Analytic Continuation of Harmonic Functions from a Circle.- § 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry.- III Inverse Problems for Differential Equations.- § 1 The Inverse Problem for a Newtonian Potential.- § 2 A Class of Nonlinear Integral Equations.- § 3 Inverse Problems for Some Non-Newtonian Potentials.- § 4 An Inverse Problem for the Wave Equation.- § 5 On a Class of Inverse Problems for Differential Equations..ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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