Moment Theory And Some Inverse Problems In Potential Theory And Heat Conduction
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Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction
Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.
Modules Over Operads and Functors
Author: Benoit Fresse
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-03-26
The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.
Operator-Valued Measures and Integrals for Cone-Valued Functions
Author: Walter Roth
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-02-05
Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions, but different approaches are used for each case. This book develops a general theory of integration that simultaneously deals with all three cases.