Search Results

You are looking at 1 - 10 of 54 items for :

  • "bounded variation" x
  • All content x
Clear All

bounded variation, Studia Sci. Math. Hungar. , 42 (2005), 235–252. MR 2146154 ( 2006a :41033) Agratini O. On the rate of convergence of some integral operators for functions of

Restricted access

References [1] Adams , C. R. , and Clarkson , J. A. , Properties of functions f(x, y) of bounded variation , Trans. Amer. Math. Soc., , 36 ( 1934 ), 711 – 730

Restricted access

Summary  

We prove that the gap seriesΣf(n k x) does not behave like an independent random series when f is a function of bounded variation with rational discontinuity.

Restricted access

Summary We discuss the existence or the existence and uniqueness of global and local Λ-bounded variation (ΛBV) solutions as well as continuous ΛBV-solutions of nonlinear Hammerstein and Volterra-Hammerstein integral equations formulated in terms of the Lebesgue integral. Since the space of functions of bounded variation in the sense of Jordan is a proper subspace of functions of Λ-bounded variation and for some class of functions φ, the space of functions of bounded φ-variation in the sense of Young is also a proper subspace of the space under consideration, our results extend known results in the literature.

Restricted access

Abstract  

In this paper definitions for “bounded variation”, “subsequences”, “Pringsheim limit points”, and “stretchings” of a double sequence are presented. Using these definitions and the notion of regularity for four dimensional matrices, the following two questions will be answered. First, if there exists a four dimensional regular matrix A such that Ay = Σk,l=1,1 ∞∞ a m,n,k,l y k,l is of bounded variation (BV) for every subsequence y of x, does it necessarily follow that x ∈ BV? Second, if there exists a four dimensional regular matrix A such that Ay ∈ BV for all stretchings y of x, does it necessarily follow that x ∈ BV? Also some natural implications and variations of the two Tauberian questions above will be presented.

Restricted access

Khan, M. K., On the Rate of Convergence of Bernstein Power Series for Functions of Bounded Variation, Journal of Approximation Theory 57 (1989), 90-103. MR 90d :41043 On the Rate of

Restricted access

Abstract  

This paper deals with three classes of functions of great importance in analysis and its applications. We construct a family of Hlder functions in the closed unit interval having two continuous parameters. Those functions are not of bounded variation for any pair of values of the Hlder constant and exponent. The construction depends on a change of variables given by a Lipschitz function with constant equal to 1. Several questions related to the concepts of genericity, surjectivity and deformability are posed at the end.

Restricted access

Резюме  

С. А. Теляковский [12] распостронил теорему Боянича [2], которая является количестбенным вариантом широко известной в классическом анализе фурье турье теореяы Дирихле-Жордана. Наша цель — расширять теорему Теляковского с одномерных на двумерные ряды фурье функций ограниченной вариации в смысле Харди и Краузе. Указанные теоремы Харди [5] и Морица [7] для таких же функций являются последствиями нашей теоремы, доказанной в ∂той стаье.

Restricted access

Abstract  

Generalized Wiener classes are considered. For these classes the exact order of Fourier coefficients with respect to the trigonometric system is established and the estimation of ‖S n(·, f)-f(·)‖C [0,2π] where S n(·, f) are the Fourier partial sums, is given. In particular, a uniform convergence criterion for the Fourier trigonometric series is obtained.

Restricted access