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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions: 100 (Graduate Texts in Mathematics) - Hardcover
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The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.
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The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk» is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.
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Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics Vol. 100)
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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics, 100)
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Hardcover. Zustand: Used; Like New. New York, 1984; yellow and white cloth covered boards; mild edge and corner wear; rear board smudged; 8vo - over 7 3/4" to 9 3/4" tall; interior pages in like new condition; Interior is clean and unmarked; Previous owner's name on front paste-down; 289 pages. Bestandsnummer des Verkäufers SKU1147867
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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
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Secaucus, New Jersey, U.S.A.: Springer Verlag, 1984
ISBN 10: 0387909257
ISBN 13: 9780387909257
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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
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Harmonic Analysis on Semigroups : Theory of Positive Definite and Related Functions
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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics, 100)
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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics, 100)
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Harmonic Analysis on Semigroups (Hardcover)
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Springer-Verlag New York Inc., New York, NY, 1984
ISBN 10: 0387909257
ISBN 13: 9780387909257
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Hardcover. Zustand: new. Hardcover. The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk is positive definite for all finite choices of elements St, . Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9780387909257
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Harmonic Analysis on Semigroups : Theory of Positive Definite and Related Functions
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