Potential Theory On Locally Compact Abelian Groups PDF Download
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Author | : C. van den Berg |
Publisher | : Springer Science & Business Media |
Total Pages | : 205 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642661289 |
Download Potential Theory on Locally Compact Abelian Groups Book in PDF, ePub and Kindle
Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients.
Author | : Christian Berg |
Publisher | : |
Total Pages | : 197 |
Release | : 1975 |
Genre | : Locally compact Abelian groups |
ISBN | : |
Download Potential Theory on Locally Compact Abelian Groups Book in PDF, ePub and Kindle
Author | : Alexander Bendikov |
Publisher | : Walter de Gruyter |
Total Pages | : 193 |
Release | : 2011-04-20 |
Genre | : Mathematics |
ISBN | : 3110876841 |
Download Potential Theory on Infinite-Dimensional Abelian Groups Book in PDF, ePub and Kindle
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. 30 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.
Author | : Sidney A. Morris |
Publisher | : Cambridge University Press |
Total Pages | : 141 |
Release | : 1977-08-04 |
Genre | : Mathematics |
ISBN | : 0521215439 |
Download Pontryagin Duality and the Structure of Locally Compact Abelian Groups Book in PDF, ePub and Kindle
These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.
Author | : David L. Armacost |
Publisher | : |
Total Pages | : 198 |
Release | : 1969 |
Genre | : Abelian groups |
ISBN | : |
Download Topics in the Character Theory of Locally Compact Abelian Groups Book in PDF, ePub and Kindle
Author | : Lawrence Adam Bruckner |
Publisher | : |
Total Pages | : 122 |
Release | : 1968 |
Genre | : Abelian groups |
ISBN | : |
Download Some Contributions to the Theory of Homogeneous Random Fields on Locally Compact Abelian Groups Book in PDF, ePub and Kindle
Author | : Josef Kral |
Publisher | : Walter de Gruyter |
Total Pages | : 513 |
Release | : 2011-10-13 |
Genre | : Mathematics |
ISBN | : 3110818574 |
Download Potential Theory - ICPT 94 Book in PDF, ePub and Kindle
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author | : Jocelyn Quaintance Jean Gallier |
Publisher | : World Scientific Publishing Company |
Total Pages | : 0 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9789811291715 |
Download Aspects of Harmonic Analysis on Locally Compact Abelian Groups Book in PDF, ePub and Kindle
"A rigorous, accessible, and self-contained introduction to the harmonic analysis of locally compact abelian groups and the mathematical underpinnings of the Fourier transform"--
Author | : Dikran Dikranjan |
Publisher | : CRC Press |
Total Pages | : 381 |
Release | : 2019-05-31 |
Genre | : Mathematics |
ISBN | : 0429530064 |
Download Abelian Groups, Module Theory, and Topology Book in PDF, ePub and Kindle
Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
Author | : David L. Armacost |
Publisher | : |
Total Pages | : 176 |
Release | : 1981 |
Genre | : Mathematics |
ISBN | : |
Download The Structure of Locally Compact Abelian Groups Book in PDF, ePub and Kindle