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Saturday, May 2, 2020 | History

2 edition of Riesz summability for double series. found in the catalog.

Riesz summability for double series.

Florence Marie Mears

# Riesz summability for double series.

## by Florence Marie Mears

Published in [n.p .
Written in English

Subjects:
• Series (mathematical)

• Edition Notes

(Reprinted from the Transactions of the American Mathematical Society, Vol. 30, No. 4, p. 686-709)

The Physical Object
Pagination[24 p.]
Number of Pages24
ID Numbers
Open LibraryOL15501746M

On the Riesz summability of Fourier series Sunouchi, Gen-ichirô, Tohoku Mathematical Journal, On the Riesz summability of Fourier series Kanno, Kôsi, Tohoku Mathematical Journal, An alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summable double sequences Findik, Gökşen, Çanak, İbrahim, and Totur Author: B. Kuttner. Ferenc Weisz, Riesz means of Fourier transforms and Fourier series on Hardy spaces Ferenc Móricz, On the maximal Fejér operator for double Fourier series of functions in Hardy spaces Ferenc Weisz, Fejér means of two-dimensional Fourier transforms on H p (ℝ × ℝ)Cited by:

series; a sufficient condition for the summability of the product of two double series to the correct sum. The proofs are similar to those of Hardy and Riesz* for the Riesz defi-nition for simple series, with such alterations as might reasonably be ex-pected because of change in . An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation.

summability is analogous to that between (a, p) and (C, a) summability. In particular 1 a, O] is the same as absolute Riesz summability /R, n. a (and therefore equivalent (Hyslop [lo]) to 1 C, a 1 summability. Bosanquet has played a major role in the application of Cesiro summability to Fourier series. Florence Marie Mears ( – December 3, completing her thesis on the "Riesz Summability for Double Series" (published in Transactions of the American Mathematical Society in ) with thesis advisor Wallie Abraham Hurwitz. Mears also published several articles and book reviews in leading mathematical journals.

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### Riesz summability for double series by Florence Marie Mears Download PDF EPUB FB2

Adams CR () Transformations of double sequences with application to Cesáro summability of double series. Bull Am Math Soc 37(10)– CrossRef zbMATH Google Scholar Cited by: 8.

In this paper we have extended the corresponding results on the Riesz summable single series to Riesz summable double series. Extensions of Riesz's Theorem.

We consider here a double series p () E am.n. m,n=Q The definitions for Cesäro and Rieszian summability of this series are analo-gous to those for simple Let —1. Extensions of Riesz's Theorem. We consider here a double series co (2. 11)E mn m,n-O The definitions for Cesaro and Rieszian summability of this series are analo-gous to those for simple series.T4 Let   H.

Bor, Some new results on absolute Riesz summability of infinite series and Fourier series, Positivity 20 (), no. 3, – Crossref Web of Science Google Scholar [5]Author: Hüseyin Bor.

is called the riesz mean of order k, type, associated with the series while is called the Riesz sum. If and when s is finite,the series. is said to be summable, to the sum s. Therefore we conclude that Riesz summability of order k and type n and Cesaro summability of same order are equivalent.

Author links open overlay panel Şebnem Yildiz. Show more. Some new results on absolute Riesz summability of infinite series and Fourier series. A note on N ̄, p n k summability factors. Int. Pure Appl. Math., 13 (), pp. Cited by: 4. and if the Fejer means of the series tend to zero, then all the coefficients a n and b n are zero.

His results on summability of trigonometric series include a generalisation of Fejér's theorem to Cesàro means of arbitrary order. He also studied the summability of power and Dirichlet series, and coauthored a book Hardy & Riesz () on the latter with G.H.

al advisor: Lipót Fejér. The method was introduced by M. Riesz for the summation of Dirichlet series. The method $(R,\lambda,k)$ is regular; when $\lambda_n=n$ it is equivalent to the Cesàro summation method $(C,k)$ (cf. Cesàro summation methods), and these methods are compatible (cf.

Compatibility of summation methods). In Section 3, we define some linear summability methods for double series and extend to double series a summability method considered by Fomin in. We give a general theorem of regularity for these methods.

Proof of Theorem 1. We first note that () v 0, 0 ∑ k = 0 ∞ ∑ l = 0 ∞ Δ 1, 1 (1 v) (k, l) = : B. Brive, C. Finet, G. Tkebuchava. RIESZ MEANS: STRONG SUMMABILITY AT THE CRITICAL INDEX We remark that for the classical Riesz means (or generalized Riesz means as-suming ﬁnite type conditions on the cosphere Σ ρ ={ξ:ρ(ξ)=1}), Theorem for the range q ≤ 2 could have been extracted from [32], although that result is notexplicitlystatedthere.

Absolute Summability of Fourier Series and Orthogonal Series Absolute Summability of Fourier Series and Orthogonal Series. Authors: Okuyama, Y. Free Preview. Buy this book eBook 18 Local property of absolute Riesz summability of fourier series. Pages Okuyama, Yasuo.

About this book Marcel Riesz () was the younger of the famed pair of mathematicians and brothers. Although Hungarian he spent most of his professional life in Sweden. He worked on summability theory, analytic functions, the moment problem, harmonic and functional analysis, potential theory and the wave : Springer-Verlag Berlin Heidelberg.

On Generalized Absolute Riesz Summability Method. On Generalized Absolute Riesz Summability Method. Bağdagül Kartal. Abstract. This paper presents a generalization of a known theorem dealing with absolute Riesz summability of infinite series to the ${\varphi}-|\bar{N},p_{n};\delta|_{k}$ : Bağdagül Kartal.

An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation.

θ-summability, which is a general summability method generated by a single function θ, and the Cesaro summability are also considered. We will prove all results except the ones that can be found in the books Grafakos [43] and Weisz [94]. For example, the results about the circular Riesz summability Cited by: Starting inErnesto Ces ro, mile Borel and others investigated well-defined methods to assign generalized sums to divergent series-including new interpretations of Euler's attempts.

Many of these summability methods easily assign to a "sum" of after all. Ces ro summa. Marcinkiewicz-θ-summability of double F ourier series Note that the second condition of (1) is satisﬁed if θ is non-increasing on (c, ∞) for some c ≥ 0 or if it has compact supp : Ferenc Weisz.

A generalization of the Riesz–Fischer theorem and we define some linear summability methods for double series and extend to double series a summability method considered by Fomin in [10].

We give a general theorem of regularity for these methods. Proof ofTheorem 1. This book contains the investigations on some properties of a subset of absolutely convergent sequence space, some general properties of the space of entire double sequences and analytic double sequences, the sequence spaces using modulus function defined on semi-normed spaces, on indexed summability methods and on Absolute Banach summability Author: Padmanava Samanta, Mahendra Misra, Umakanta Misra.ity, the absolute Riesz summability, absolute generalized Ces aro summabilit y, abso- lute Euler summability of an orthogonal series has been studied by many authors.Some applications to Birkhoff series are given.

AMS subject classifications. 40 G05, 40 G99, 34 B25 0. Introduction In his well-known paper [13], M.H. Stone introduced Riesz means in order to derive summability results for eigenfunction expansions (Birkhoff series) associated with certain generally non-selfadjoint boundary value problems.