Books in Functions of a complex variable

Complex Analysis in Locally Convex Spaces

1st Edition
Volume 57
August 18, 2011
S. Dineen
English
eBook
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Nine Introductions in Complex Analysis - Revised Edition

1st Edition
Volume 208
September 6, 2007
Sanford L. Segal
English
eBook
9 7 8 0 0 8 0 5 5 0 7 6 3

The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective.

Complex Numbers in n Dimensions

1st Edition
Volume 190
June 20, 2002
S. Olariu
English
eBook
9 7 8 0 0 8 0 5 2 9 5 8 5

Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functionsof the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

Inverse Spectral Theory

1st Edition
Volume 130
March 16, 1987
Jurgen Poschel
English
eBook
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A First Course in Stochastic Processes

2nd Edition
March 28, 1975
Samuel Karlin + 1 more
English
Hardback
9 7 8 0 1 2 3 9 8 5 5 2 1

The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other. The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.

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