The Problem of MomentsAmerican Mathematical Soc., 31 gru 1943 - 140 The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas. |
Spis treści
A GENERAL THEORY OF THE PROBLEM OF MOMENTs 1 22 | 1 |
THEORY OF THE HAMBURGER MOMENT PROBLEM 23 76 | 23 |
VARIOUS MODIFICATIONS OF THE MOMENT PROBLEM 77105 | 77 |
APPROXIMATE QUADRATUREs 106126 | 106 |
BIBLIOGRAPHY 127138 | 127 |
SUPPLEMENTARY BIBLIOGRAPHY _ 139141 | 139 |
Inne wydania - Wyświetl wszystko
The Problem of Moments James Alexander Shohat,James Shohat,Jacob David Tamarkin,American Mathematical Society Podgląd niedostępny - 1943 |
Kluczowe wyrazy i wyrażenia
Achyeser and Krein American Mathematical Society analogous analytic approximate quadrature formula axis of reals Bernstein polynomial bounded variation circle coefficients completely monotonic Comptes Rendus continued fraction converges COROLLARY corresponding defined definite degree g discussion distribution function find finite interval first fixed function f function of order half-plane Hamburger moment problem Hausdorff Hence implies indeterminate inequality integral l'Académie des Sciences l’Académie Lemma moment problem 2.1 Moment-Problem monotonic sequence necessary and sufficient necessary and suflicient non-negative orthogonal polynomials Parseval formula holds polynomial of degree polynomial of order positive problem 2.1 problem is determined Problem of Moments problème des moments proof of Theorem properties quadratic form real number reduced moment problem Riesz roots satisfied satisfying the condition sector sequence of moments shows solution Mt Stieltjes moment problem substantially equal suffices sufficient condition sufficiently large suflicient condition Tchebychefi theory tion uniformly uniquely determined Vitali Theorem Widder