Markov Operators, Positive Semigroups and Approximation Processes

ISBN-13: 9783110372748 / Angielski / Twarda / 2014 / 325 str.

Francesco Altomare;Mirella Cappelletti;Vita Leonessa

Opis

In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.

Recenzje

"The authors successfully succeed in demonstrating that the relationship between approximation theory and the theory of C₀-semigroups of linear operators and evolution equations represents a fascinating and powerful mathematical theory that succeeds in solving problems related to potential theory, partial differential equations, and mathematical physics. [...]The material, forming a perfect integral whole, offers information that puts the reader at the forefront of current research and determines fruitful directions for future advanced studies. The architecture of the monograph also includes substantial motivation and examples for key results. Clarity of the text and rigorous proofs represent other features of this book. We believe that the reader will also appreciate the final section of each chapter named notes and comments. [...] In closing, it is worth mentioning that the monograph may clearly serve as a perfect basis both for researchers and graduate students in pure and applied mathematics who are interested in a modern approach to the theory of positive C₀-semigroups of operators and their connections with approximation processes." Mathematical Reviews

"This book is a welcome contribution to the topic of approximation theory for solutions of partial differential equations with degenerate coefficients. It is written as - and meant to be - a standard reference for researchers working in this field, and it will certainly become one." Zentralblatt für Mathematik

O autorze

F. Altomare, M. C. Montano, U. of Bari, It.; V. Leonessa, U.d.S. della Basilicata, Potenza, It.; I. Rasa, T.U. of Cluj-Napoca, Rom.