منابع مشابه
Matrix transformations and Walsh's equiconvergence theorem
In 1977, Jacob defines Gα, for any 0 ≤ α <∞, as the set of all complex sequences x such that limsup|xk|1/k ≤ α. In this paper, we apply Gu −Gv matrix transformation on the sequences of operators given in the famous Walsh’s equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the Gu −Gv matrix transformation of the dif...
متن کاملOn a Theorem of J. L. Walsh
Abel, Bord, Cesâro, Holder and Hausdorff, Journal d'Analyse Mathématique vol. 3 (1953-1954) pp. 346-381. 2. -, On a converse of Abel's theorem, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 244-256. 3. W. W. Rogosinski, On Hausdorff methods of summability, Proc. Cambridge Philos. Soc. vol. 38 (1942) pp. 166-192. 4. O. Szász, On the product of two summability methods, Annales de la Société Polonaise ...
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A recent result of Muckenhoupt concerning the convergence of the expansion of an arbitrary function in terms of the Hermite series of orthogonal polynomials is generalised to a class of orthogonal expansions which arise from an eigenfunction problem associated with a second-order linear differential equation.
متن کاملOn Walsh code assignment
The paper considers the problem of orthogonal variable spreading Walsh-code assignments. The aim of the paper is to provide assignments that can avoid both complicated signaling from the BS to the users and blind rate and code detection amongst a great number of possible codes. The assignments considered here use a partition of all users into several pools. Each pool can use its own codes that ...
متن کاملOn Walsh-fourier Series^)
Every function f(x) which is of period 1 and Lebesgue integrable on [0, 1 ] may be expanded in a Walsh-Fourier series(3), f(x)~ ?.?=n ak\pk(x), where ak=fof(x)ypk(x)dx, k=0, 1, 2, • • • . Fine exhibited some of the basic similarities and differences between the trigonometric orthonormal system and the Walsh system. He identified the Walsh functions with the full set of characters of the dyadic ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1988
ISSN: 0021-9045
DOI: 10.1016/0021-9045(88)90047-0