Results 241 to 250 of about 8,078 (282)
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2000
Abstract After having become acquainted in Chapter 2 with several inclusion, comparison and consistency results it is time to put some life into the theory by considering (classes of) examples of summability methods. In this way we shall have the opportunity to apply theorems, proved in Chapter 2, to special matrix methods. In particular,
Johann Boos, Peter Cass
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Abstract After having become acquainted in Chapter 2 with several inclusion, comparison and consistency results it is time to put some life into the theory by considering (classes of) examples of summability methods. In this way we shall have the opportunity to apply theorems, proved in Chapter 2, to special matrix methods. In particular,
Johann Boos, Peter Cass
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2017
In the current chapter, we introduce some special methods of summability, viz. the Abel method, the Weighted Mean method, the Euler method and the \((M, \lambda _n)\) or Natarajan method, and study their properties extensively. The connection between the Abel method and the Natarajan method is brought out.
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In the current chapter, we introduce some special methods of summability, viz. the Abel method, the Weighted Mean method, the Euler method and the \((M, \lambda _n)\) or Natarajan method, and study their properties extensively. The connection between the Abel method and the Natarajan method is brought out.
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On Some Triangular Summability Methods
American Journal of Mathematics, 1947It is to be noted that Bn (x) is defined by taking the first n + 1 terms of the series defining the function *J(x) ; the summability method is then constructed with the sequence {x.n}. As set forth in the aforementioned paper of Szasz,2 the regularity of either method (1. 1) or (1. 2) does not imply the regularity of the other method. On the other hand,
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Summability Methods in Perturbation Theory
Journal of Mathematical Physics, 1970The Mittag-Leffler summability method is applied to operator-valued analytic functions and a corresponding procedure for perturbation theory is derived, which has a bigger region of convergence. This region is explicitly described.
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On Scales of Summability Methods
Mathematische Nachrichten, 1995AbstractIn this paper we consider generalized Nörlund methods (Nαp), α > ‐1, power series methods (Jp) and the iteration product of two such methods. A particular case is that of the Cesaro means (Cα) with corresponding power series method (A), i.e., Abel's method.
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Summability Methods on Matrix Spaces
Canadian Journal of Mathematics, 1961The matrix spaces under consideration are the four main types of irreducible bounded symmetric domains given by Cartan (5). Let z = (zjk) be a matrix of complex numbers, z' its transpose, z* its conjugate transpose and I = I(n) the identity matrix of order n.
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Borel’s Methods of Summability
1994Abstract Summability methods are transformations that map sequences (or functions) to sequences (or functions). A prime requirement for a "good" summability method is that it preserves convergence. Unless it is the identity transformation, it will do more: it will transform some divergent sequences to convergent sequences.
Bruce Shawyer, Bruce Watson
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ERGODIC THEOREMS AND SUMMABILITY METHODS
The Quarterly Journal of Mathematics, 1987Given: a regular summation method \((a_{n,m})_{n,m}\) such that \(\sum^{\infty}_{k=m}| a_{n,m+1}-a_{n,m}| \to 0\) uniformly in n and a sequence \((T_ n)_ n\) of bounded operators, chosen independently on a Banach space X. The author investigates conditions under which \(\lim_{n\to \infty}\sum^{\infty}_{m=1}a_{n,m}T_ m,...,T_ 1(x)\) (x\(\in X)\) exists ...
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Mathematical Proceedings of the Cambridge Philosophical Society, 1985
Let Σan be a given infinite series with partial sums sn, and rn = nan. By and we denote the nth Cesáro means of order α (α –1) of the sequences (sn) and (rn), respectively. The series Σan is said to be absolutely summable (C, a) with index k, or simply summable |C, α|k, k ≥ 1 ...
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Let Σan be a given infinite series with partial sums sn, and rn = nan. By and we denote the nth Cesáro means of order α (α –1) of the sequences (sn) and (rn), respectively. The series Σan is said to be absolutely summable (C, a) with index k, or simply summable |C, α|k, k ≥ 1 ...
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