The problem of L1-convergence of the Fourier cosine series (1.1) has been settled for various special classes of coefficients. Young [6] found that an logn= o(1), n→∞ is a necessary and sufficient condition for cosine series with convex (∆an ≥ 0) coefficients, and Kolmogorov [5] extended this result to the cosine series with quasi-convex ( ∑∞ n=1n|∆an−1| < ∞) coefficients. Later, Garrett and St...

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay ...

be the Fourier cosine series. The problem of L-convergence of the Fourier cosine series (1.1) has been settled for various special classes of coefficients. Young [9] found that an logn = o(1), n → ∞ is a necessary and sufficient condition for the L-convergence of the cosine series with convex (△an ≥ 0) coefficients, and Kolmogorov [8] extended this result to the cosine series with quasi-convex ( ∞

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

A classic result, in its early form due to Cox [2], states that if A is a normed algebra with a unity denoted by 1 and a is an element of A such that supn∈N ‖a− 1‖ < 1, then a = 1. Cox’s version concerned the case of square matrices of a given size. This was later extended to bounded operators on Hilbert space by Nakamura and Yoshida [6], and to an arbitrary normed algebra by Hirschfeld [4] and...

In the past decade, the advancement in data communications was significant during explosive growth of the Internet, which led to the demand for using multimedia in portable devices. Video and Audio data streams require a huge amount of bandwidth to be transferred in an uncompressed form. The objective of this paper is to minimize the number of bits required to represent an image and also the ac...

Abstract Morphological prior information incorporated with the discrete cosine transformation (DCT) based electrical impedance tomography (EIT) algorithm can improve interpretability of EIT reconstructions in clinical applications. However, an outdated structural yield a misleading reconstruction compromising accuracy diagnosis and appropriate treatment decision. In this contribution, we propos...

In this paper we intend to present IEEE-754 format and comparison of Cosine Trigonometric functions used in Discrete Cosine Transform (DCT) in terms of hardware design. Here we find the cosine value by C language and Hardware Description Language (HDL) and checking the error for DCT.