Banach Spaces Analytic

Song, Renming/Davis, Burgess: Selected Works of Donald L. Burkholder Selected Works in Probability and Statistics, SPRINGER, BERLIN, 011 ISBN: 1441972447
font face=Arial This book chronicles Donald Burkholder's thirty-five year study of martingales and its consequences. Here are some of the highlights.Pioneering work by Burkholder and Donald Austin on the discrete time martingale square function led to Burkholder and Richard Gundy's proof of inequalities comparing the quadratic variations and maximal functions of continuous martingales, inequalities which are now indispensable tools for stochastic analysis. Part of their proof showed how novel distributional inequalities between the maximal function and quadratic variation lead to inequalities for certain integrals of functions of these operators. The argument used in their proof applies widely and is now called the Burkholder-Gundy good lambda method. This uncomplicated and yet extremely elegant technique, which does not involve randomness, has become important in many parts of mathematics.The continuous martingale inequalities were then used by Burkholder, Gundy, and Silverstein to prove the converse of an old and celebrated theorem of Hardy and Littlewood. This paper transformed the theory of Hardy spaces of analytic functions in the unit disc and extended and completed classical results of Marcinkiewicz concerning norms of conjugate functions and Hilbert transforms. While some connections between probability and analytic and harmonic functions had previously been known, this single paper persuaded many analysts to learn probability.These papers together with Burkholder's study of martingale transforms led to major advances in Banach spaces. A simple geometric condition given by Burkholder was shown by Burkholder, Terry McConnell, and Jean Bourgain to characterize those Banach spaces for which the analog of the Hilbert transform retains important properties of the classical Hilbert transform.Techniques involved in Burkholder's usually successful pursuit of best constants in martingale inequalities have become central to extensive recent research into two well- known open problems, one involving the two dimensional Hilbert transform and its connection to quasiconformal mappings and the other a conjecture in the calculus of variations concerning rank-one convex and quasiconvex functions.This book includes reprints of many of Burkholder's papers, together with two commentaries on his work and its continuing impact. /font

NEUBUCH! 2010. XX, 580 S. 279 mm 279 mm x 210 mm; Selected Works in Probability and Statistics

[KW: Statistik]

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Sauvigny, Friedrich: Partial Differential Equations Functional Analytic Methods, SPRINGER, BERLIN, Mai 2011, Besorgungstitel - vorauss. Lieferzeit 3-5 Tage. ISBN: 3540344616
This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.

NEUBUCH! 2006. XIV, 392 p. 23,5 cm 235 mm x 155 mm x 24 mm; Universitext

[KW: Partielle Differenzialgleichungen]

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Polat, Faruk: On the Generalizations and Properties of Abramovich-Wickstead Spaces Dominated Operators on Abramovich-Wickstead Spaces, LAP LAMBERT ACADEMIC PUBLISHING, Oktober 2011, Besorgungstitel - vorauss. Lieferzeit 3-5 Tage. ISBN: 3846518506
The present monograph concerns with new types of Abramovich-Wickstead spaces,the elements of which are the sums of real-valued (or vector valued in general) continuous functions and discrete functions on a compact Hausdorff space without isolated points, and analytic representations of different classes of dominated operators on these spaces. Although it is primarily based on the Ph.D. thesis of the author, the monograph provides further results and information on recent advances about that topic. The notion of a dominated operator was invented in the 1930s by L. V. Kantorovich. The idea of dominated operator can be stated as follows: if an operator under consideration is dominated by another operator, called a dominant, then the properties of the latter have a substantail influence on the properties of the former. Thus, operators that have nice dominants must posses nice properties. In this book, we are interested in giving some results concerning Banach space valued dominated operators on Abramovich-Wickstead spaces.

NEUBUCH! Aufl. 2011. 112 S. 220 mm x 150 mm x 7 mm

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Hoffman, Kenneth. Banach spaces of analytic functions. (= Prentice-Hall series in modern analysis). Prentice Hall, Englewood Cliffs 1962.
Beiliegt: Der leicht beschädigte und lichtrandige Original-Schutzumschlag. -

XIII, 217 S., Groß 8°, Original-Pappband (Hardcover), Bibliotheks-Exemplar (ordungsgemäß entwidmet), Stempel auf Titel, insgesamt gutes und innen sauberes Exemplar,

[KW: Mathematik]

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