s of MMA2015, May 26–29, 2015, Sigulda, Latvia c © 2015 ON HIGHER DEGREE F-TRANSFORMS BASED ON B-SPLINES MARTINS KOKAINIS and SVETLANA ASMUSS 1 Department of Mathematics, University of Latvia Zeļļu iela 8, R̄ıga, LV-1002, Latvia 2 Institute of Mathematics and Computer Science, University of Latvia Raiņa bulvāris 29, R̄ıga, LV-1459, Latvia E-mail: [email protected], [email protected] The ...

The generalized Bochner-Riesz operator SR,λ may be defined as Sf(x) = F−1 [( 1− ρ R )λ + f̂ ] (x) where ρ is an appropriate distance function and F−1 is the inverse Fourier transform. The sharp bound ‖Sf‖L4(R2×R2) ≤ C‖f‖L4(R2×R2) is shown for the distance function ρ(ξ′, ξ”) = max{|ξ′|, |ξ′′|}. This is a rough distance function corresponding to the R4 cylinder analog {(x1, x2, x3, x4) ∈ R4, x1+ x...

The fuzzy transform (F-transform) is ubiquitous in different research fields and applications, such as image data compression, mining, knowledge discovery, the analysis of linguistic expressions. As a generalization F-transform, this article, we introduce continuous F-transform its inverse, an integral operator induced by kernel function. Through relation between membership functions kernels, s...

A relationship between the discrete F-transform and aggregation functions is analyzed. We show that the discrete F-transform (direct or inverse) can be associated with a set of linear aggregation functions that respect a fuzzy partition of a universe. On the other side, we discover conditions that should be added to a set of linear aggregation functions in order to obtain the discrete F-transfo...

The classical Fourier transform Fcl is an isomorphism of the Schwartz space S(Rk) onto itself. The space C∞ c (Rk) of smooth functions with compact support is dense in S(Rk), and the classical Paley-Wiener theorem characterises the image of C∞ c (R k) under Fcl as rapidly decreasing functions having an holomorphic extension to Ck of exponential type. Since Rk is self-dual, the same theorem also...

the radial trace transform was introduced by the stanford exploration project many years ago (ottolini, 1979 and claerbout, 1983), primarily for use in migration and imaging applications. it has been shown subsequently, because of its particular geometry, to be very useful for wavefield separation (claerbout, 1983) and coherent noise attenuation (henley, 1999). the radial trace transform, unlik...

Abstract. The aim of this paper is to establish an analogue of Logvinenko-Sereda’s theorem for the Fourier-Bessel transform (or Hankel transform) Fα of order α > −1/2. Roughly speaking, if we denote by PWα(b) the Paley-Wiener space of L -functions with FourierBessel transform supported in [0, b], then we show that the restriction map f → f |Ω is essentially invertible on PWα(b) if and only if Ω...

The paper is devoted to the smoothing of discrete functions using the fuzzy transform (shortly, Ftransform) introduced by Perfilieva in [1]. We generalize a smoothing filter based on the fuzzy transform proposed in [2] to obtain a better control on the smoothed functions. For this purpose, a generalization of the concept of fuzzy partition is suggested and the smoothing filter is defined as a c...

[08.3] Compute e−πx 2 ∗ e−πx2 and sinx x ∗ sinx x . (Be careful what you assert: sin x x is not in L (R).) Discussion: The idea is to invoke f ∗ g = (f̂ · ĝ)̂ for even functions f, g ∈ L, since for even functions the inverse Fourier transform is the same as the forward Fourier transform. Conveniently, Gaussians are in L ∩ L, and have Fourier transforms which are again Gaussians: ̂ e−πax(ξ) = 1 √ a...

This paper describes an implementation of the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). We show how the computation of the DFT and IDFT may be performed in Java and show why such operations are typically considered slow. This is a multi-part paper, in part 2, we discuss a speed up of the DFT and IDFT using a class of algorithms known as the FFT (Fast Fo...