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This research monograph gives a detailed account of a theory which
is mainly concerned with certain classes of degenerate differential
operators, Markov semigroups and approximation processes. These
mathematical objects are generated by arbitrary Markov operators
acting on spaces of continuous functions defined on compact convex
sets; the study of the interrelations between them constitutes one
of the distinguishing features of the book. Among other things,
this theory provides useful tools for studying large classes of
initial-boundary value evolution problems, the main aim being to
obtain a constructive approximation to the associated positive
C0-semigroups by means of iterates of suitable positive
approximating operators. As a consequence, a qualitative analysis
of the solutions to the evolution problems can be efficiently
developed. The book is mainly addressed to research mathematicians
interested in modern approximation theory by positive linear
operators and/or in the theory of positive C0-semigroups of
operators and evolution equations. It could also serve as a
textbook for a graduate level course.
The series is devoted to the publication of monographs and
high-level textbooks in mathematics, mathematical methods and their
applications. Apart from covering important areas of current
interest, a major aim is to make topics of an interdisciplinary
nature accessible to the non-specialist. The works in this series
are addressed to advanced students and researchers in mathematics
and theoretical physics. In addition, it can serve as a guide for
lectures and seminars on a graduate level. The series de Gruyter
Studies in Mathematics was founded ca. 35 years ago by the late
Professor Heinz Bauer and Professor Peter Gabriel with the aim to
establish a series of monographs and textbooks of high standard,
written by scholars with an international reputation presenting
current fields of research in pure and applied mathematics. While
the editorial board of the Studies has changed with the years, the
aspirations of the Studies are unchanged. In times of rapid growth
of mathematical knowledge carefully written monographs and
textbooks written by experts are needed more than ever, not least
to pave the way for the next generation of mathematicians. In this
sense the editorial board and the publisher of the Studies are
devoted to continue the Studies as a service to the mathematical
community. Please submit any book proposals to Niels Jacob. Titles
in planning include Flavia Smarazzo and Alberto Tesei, Measure
Theory: Radon Measures, Young Measures, and Applications to
Parabolic Problems (2019) Elena Cordero and Luigi Rodino,
Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert,
Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational
Models for Fractional Calculus, second edition (2020) Mariusz
Lemanczyk, Ergodic Theory: Spectral Theory, Joinings, and Their
Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic
Complex Manifolds (2021) Miroslava Antic, Joeri Van der Veken, and
Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds
of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu,
Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference
Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi
Miyanishi, Affine Space Fibrations (2022)
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