REST BOUNDED SECOND VARIATION SEQUENCES AND p-TH POWER INTEGRABILITY OF SOME FUNCTIONS RELATED TO SUMS OF FORMAL TRIGONOMETRIC SERIES
نویسنده
چکیده
Abstract. In this paper we have studied p-th power integrability of functions sinxg(x) and sinxf(x) with a weight, where g(x) and f(x) denote the formal sum functions of sine and cosine trigonometric series respectively. This study may be taken as a continuation for some recent foregoings results proven by L. Leindler [3] and S. Tikhonov [7] employing the so-called rest bounded second variation sequences.
منابع مشابه
On Integrability of Functions Defined by Trigonometric Series
The goal of the present paper is to generalize two theorems of R.P. Boas Jr. pertaining to L (p > 1) integrability of Fourier series with nonnegative coefficients and weight x . In our improvement the weight x is replaced by a more general one, and the case p = 1 is also yielded. We also generalize an equivalence statement of Boas utilizing power-monotone sequences instead of {n}.
متن کاملLinear Methods Which Sum Sequences of Bounded Variation
A complex sequence {zp} is said to be of bounded variation provided 2|zp —zP+i\ < oo. In this paper we show that a matrix which sums every sequence of bounded variation also sums a convergent sequence not of bounded variation (Theorem 1). Indeed, if M is a countable set of matrices, each of which sums every sequence of bounded variation, then there is a convergent sequence not of bounded variat...
متن کاملReciprocal Sums of lth Power of Generalized Binary Sequences with Indices
Recently in [5], the author considered certain reciprocal sums of general second order recurrence fWng : In this paper, we generalize the results of Xi and we give some new results for the reciprocal sums of l-th power of general second order recurrence fWkng for arbitrary positive integer k: 1. Introduction Let a; b; P and Q integers such that PQ 6= 0 and P 2 4Q 6= 0: De ne the sequence fWng a...
متن کاملOn Bounded Linear Functional Operations* By
The set of all bounded linear functional operations on a given vector spacej plays an important role in the consideration of linear functional operations. For the sake of greater definiteness it is desirable to know the form of such operations and a space determined thereby. This problem has been solved for a number of spaces, for instance, all continuous functions on a bounded closed interval,...
متن کاملLazy Processing and Optimization of Discrete Sequences
We construct a small arithmetic package operating on discrete sequences: u0, u1, u2, . . . treated as single mathematical entities. Applying functions to sequences by the generalized map, or adding them element-wise is quite trivial, but if the sequences are regular, e.g. if they are arithmetic or geometric progressions, a much more compact and in several cases much more efficient representatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015