Expansions

Expansions
Author: Axel Kristinsson
Publisher: ReykjavíkurAkademían
Total Pages: 383
Release: 2010
Genre: Civilization, Western
ISBN: 9979992212

Lectures on Hermite and Laguerre Expansions. (MN-42), Volume 42

Lectures on Hermite and Laguerre Expansions. (MN-42), Volume 42
Author: Sundaram Thangavelu
Publisher: Princeton University Press
Total Pages: 216
Release: 2020-06-16
Genre: Mathematics
ISBN: 0691213925

The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.

Asymptotic Expansions

Asymptotic Expansions
Author: A. Erdélyi
Publisher: Courier Corporation
Total Pages: 118
Release: 2012-04-27
Genre: Mathematics
ISBN: 0486155056

Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.

Asymptotic Expansions of Integrals

Asymptotic Expansions of Integrals
Author: Norman Bleistein
Publisher: Courier Corporation
Total Pages: 453
Release: 1986-01-01
Genre: Mathematics
ISBN: 0486650820

Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Chaos Expansions, Multiple Wiener-Ito Integrals, and Their Applications

Chaos Expansions, Multiple Wiener-Ito Integrals, and Their Applications
Author: Christian Houdre
Publisher: CRC Press
Total Pages: 396
Release: 1994-04-05
Genre: Mathematics
ISBN: 9780849380723

The study of chaos expansions and multiple Wiener-Ito integrals has become a field of considerable interest in applied and theoretical areas of probability, stochastic processes, mathematical physics, and statistics. Divided into four parts, this book features a wide selection of surveys and recent developments on these subjects. Part 1 introduces the concepts, techniques, and applications of multiple Wiener-Ito and related integrals. The second part includes papers on chaos random variables appearing in many limiting theorems. Part 3 is devoted to mixing, zero-one laws, and path continuity properties of chaos processes. The final part presents several applications to stochastic analysis.

Asian Expansions

Asian Expansions
Author: Geoff Wade
Publisher: Routledge
Total Pages: 420
Release: 2014-10-17
Genre: History
ISBN: 1135043523

Asia as we know it today is the product of a wide range of polity expansions over time. Recognising the territorial expansions of Asian polities large and small through the last several millennia helps rectify the fallacy, long-held and deeply entrenched, that Asian polities have been interested only in the control of populations, not in expanding their command of territory. In countering this misapprehension, this book suggests that Asian polities have indeed been concerned with territorial control and expansion over time, whether for political or strategic advantage, trade purposes, defence needs, agricultural expansion or increased income through taxation. The book explores the historical experiences of a set of polity expansions within Asia, specifically in East and Southeast Asia, and, by examining the motivations, mechanisms, processes, validations and limitations of these Asian territorial expansions, reveals the diverse avenues by which Asian polities have grown. The chapters draw on these historical examples to highlight the connections between Asian polity expansion and centralised political structures, and this aids in a broader and more comprehensive understanding of Asian political practice, both past and present. Through these chapter studies and the integrative introduction, the book interrogates key concepts such as imperialism and colonialism, and the applicability and relevance of such terminology in Asian contexts, both historical and contemporary. Comparisons and contrasts with European historical expansions are also suggested. This book will be welcomed by students and scholars of Asian history, as well as by those with an interest in Asian interactions, international relations, polity expansion, Asia--Europe historical comparisons and globalisation.

Hadamard Expansions and Hyperasymptotic Evaluation

Hadamard Expansions and Hyperasymptotic Evaluation
Author: R. B. Paris
Publisher: Cambridge University Press
Total Pages: 252
Release: 2011-03-24
Genre: Mathematics
ISBN: 1107002583

Describes a new asymptotic method of high-precision evaluation of certain integrals, related to the classical method of steepest descents.

Integral Expansions Related to Mehler-Fock Type Transforms

Integral Expansions Related to Mehler-Fock Type Transforms
Author: B N Mandal
Publisher: CRC Press
Total Pages: 144
Release: 2020-11-25
Genre: Mathematics
ISBN: 1000115224

An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.