A robust double exponential formula for Fourier-type integrals

A Double Exponential Formula for the Fourier Transforms

In this paper, we propose a new and efficient method that is applicable for the computation of the Fourier transform of a function which may possess a singular point or slowly converge at infinity. The proposed method is based on a generalization of the method of the double exponential (DE) formula; the DE formula is a powerful numerical quadrature proposed by H. Takahasi and M. Mori in 1974 [1...

a cauchy-schwarz type inequality for fuzzy integrals

نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.

On Approximating Hard Integrals with the Double-Exponential Formula

Approximating I#PART = ́ 1 0 ∏ n k=1 cos (xkπt) dt to within an accuracy of 2 −n where the input integers {xk} n k=1 are given in binary radix, is equivalent to counting the number of equal-sum partitions of the integers {xk} and is thus a #P problem. Similarly, integrating this function from zero to infinity and deciding whether the result is either zero or infinity is an NP-Complete problem. E...

Fourier Transformation Method for Computing NMR Integrals over Exponential Type Functions

A Weyl Type Formula for Fourier Spectra and Frames

We prove qualitative and quantitative results concerning the asymptotic density in dilates of centered convex bodies of the frequency vectors of orthogonal exponential bases and frames associated to bounded domains in Euclidean space.