Author: Irwin E. Schochetman
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 0

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Author: Irwin E. Schochetman
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author:
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 120

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Author: Irwin E. Schochetman
Publisher: American Mathematical Soc.
ISBN: 0821822020
Category : Mathematics
Languages : en
Pages : 130

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The purpose of this memoir is twofold: to extend the notions of kernel and integral operator to the context of continuous sums of Banach spaces; and to extend to this setting, certain well-known conditions for an integral operator to be compact, Hilbert-Schmidt and trace-class.

Author: Irwin E. Schochetman
Publisher: American Mathematical Soc.
ISBN: 0821822071
Category : Mathematics
Languages : en
Pages : 66

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The primary purpose of this memoir is to give a realization of the representation [italic]U of a locally compact group [italic]G, induced from a representation [italic]L of a closed subgroup [italic]H, on a continuous sum of Banach spaces over the coset space [italic]G/[italic]H.

Author: A.G. Kusraev
Publisher: Springer Science & Business Media
ISBN: 9401593493
Category : Mathematics
Languages : en
Pages : 456

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The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another operator (equation), called a dominant or majorant, then the properties of the latter have a substantial influence on the properties of the former . Thus, operators or equations that have "nice" dominants must possess "nice" properties. In other words, an operator with a somehow qualified dominant must be qualified itself. Mathematical tools, putting the idea of domination into a natural and complete form, were suggested by L. V. Kantorovich in 1935-36. He introduced the funda mental notion of a vector space normed by elements of a vector lattice and that of a linear operator between such spaces which is dominated by a positive linear or monotone sublinear operator. He also applied these notions to solving functional equations. In the succeedingyears many authors studied various particular cases of lattice normed spaces and different classes of dominated operators. However, research was performed within and in the spirit of the theory of vector and normed lattices. So, it is not an exaggeration to say that dominated operators, as independent objects of investigation, were beyond the reach of specialists for half a century. As a consequence, the most important structural properties and some interesting applications of dominated operators have become available since recently.

Author: Solomon G. Mikhlin
Publisher: Springer Science & Business Media
ISBN: 9783540159674
Category : Mathematics
Languages : en
Pages : 530

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The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.

Author:
Publisher:
ISBN:
Category : Operator theory
Languages : en
Pages : 652

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Author: Semën Samsonovich Kutateladze
Publisher: Springer Science & Business Media
ISBN: 9401143056
Category : Mathematics
Languages : en
Pages : 312

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Nonstandard methods of analysis consist generally in comparative study of two interpretations of a mathematical claim or construction given as a formal symbolic expression by means of two different set-theoretic models: one, a "standard" model and the other, a "nonstandard" model. The second half of the twentieth century is a period of significant progress in these methods and their rapid development in a few directions. The first of the latter appears often under the name coined by its inventor, A. Robinson. This memorable but slightly presumptuous and defiant term, non standard analysis, often swaps places with the term Robinsonian or classical non standard analysis. The characteristic feature of Robinsonian analysis is a frequent usage of many controversial concepts appealing to the actual infinitely small and infinitely large quantities that have resided happily in natural sciences from ancient times but were strictly forbidden in modern mathematics for many decades. The present-day achievements revive the forgotten term infinitesimal analysis which reminds us expressively of the heroic bygones of Calculus. Infinitesimal analysis expands rapidly, bringing about radical reconsideration of the general conceptual system of mathematics. The principal reasons for this progress are twofold. Firstly, infinitesimal analysis provides us with a novel under standing for the method of indivisibles rooted deeply in the mathematical classics.

Author: Konrad Jörgens
Publisher: Pitman Advanced Publishing Program
ISBN:
Category : Mathematics
Languages : en
Pages : 400

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