Related papers: On absolute convergence of multiple Fourier integr…
The conditions for convergence of square and rectangular Fejer means of functions on the infinite dimensional torus were obtained, also a generalization of the results for the case of abstract measure spaces was formulated.
We extend the result of K. Karlander [Math. Scand. 80 (1997)] regarding finite dimensionality of spaces of absolutely convergent Fourier transforms.
The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions $f\in$ Lip1 class provides absolute convergence of Fourier series. In particular we found…
We define a compact version of the Hilbert transform, which we then use to write explicit expressions for the partial sums and remainders of arbitrary Fourier series. The expression for the partial sums reproduces the known result in terms…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…
We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.
In this paper we present results on convergence and Ces\`{a}ro summability of Multiple Fourier series of functions of bounded generalized variation.
In this paper, we study the inversion formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an inversion formula which is known in engineering. We show that the integral involved in the formula…
In this paper, we have obtained a necessary and suffcient condition for the series.
A new complete invariant for acyclic graphs is presented
In the present paper, we give a brief review of $L^{1}$-convergence of trigonometric series. Previous known results in this direction are improved and generalized by establishing a new condition.
Let $ f:(0,\infty)\rightarrow \Bbb{R} $ be a completely monotonic function. In this paper, we present some properties of this functions and several new classes of completely monotonic functions. We also give some special functions such that…
Several notions of "analytic" functor introduced recently in the literature fit into the graphic fourier transform context presented in [D].
In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
In this note we consider the Fourier expansion of the Ferrers function P of the first kind. We determine its mode of convergence.
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…
In the main part of the paper, on the basis of contour integration of complex meromorphic functions whose singularities lie onto an integration contour, in the first step, a concept of improper integrals absolute existence of meromorphic…