The inverse Laplace transform of the product of two modified Bessel functions where n=1, 2, 3,...
F. M. Ragab (1963)
Annales Polonici Mathematici
Similarity:
F. M. Ragab (1963)
Annales Polonici Mathematici
Similarity:
David Grow (1987)
Colloquium Mathematicae
Similarity:
Saifallah Ghobber, Philippe Jaming (2014)
Studia Mathematica
Similarity:
The aim of this paper is to prove new uncertainty principles for integral operators with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function is highly localized near a single point then (f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function and...
B. Hollenbeck, N. J. Kalton, I. E. Verbitsky (2003)
Studia Mathematica
Similarity:
We determine the norm in , 1 < p < ∞, of the operator , where and are respectively the cosine and sine Fourier transforms on the positive real axis, and I is the identity operator. This solves a problem posed in 1984 by M. S. Birman [Bir] which originated in scattering theory for unbounded obstacles in the plane. We also obtain the -norms of the operators aI + bH, where H is the Hilbert transform (conjugate function operator) on the circle or real line, for arbitrary real...
E. Ferreyra, T. Godoy, M. Urciuolo (2004)
Studia Mathematica
Similarity:
Let φ:ℝ² → ℝ be a homogeneous polynomial function of degree m ≥ 2, let Σ = (x,φ(x)): |x| ≤ 1 and let σ be the Borel measure on Σ defined by where B is the unit open ball in ℝ² and dx denotes the Lebesgue measure on ℝ². We show that the composition of the Fourier transform in ℝ³ followed by restriction to Σ defines a bounded operator from to for certain p,q. For m ≥ 6 the results are sharp except for some border points.
Yuichi Kanjin (2001)
Studia Mathematica
Similarity:
We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space , 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on , 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of .
S. Thangavelu (2002)
Colloquium Mathematicae
Similarity:
Let G be a semisimple Lie group with Iwasawa decomposition G = KAN. Let X = G/K be the associated symmetric space and assume that X is of rank one. Let M be the centraliser of A in K and consider an orthonormal basis of L²(K/M) consisting of K-finite functions of type δ on K/M. For a function f on X let f̃(λ,b), λ ∈ ℂ, be the Helgason Fourier transform. Let be the heat kernel associated to the Laplace-Beltrami operator and let be the Kostant polynomials. We establish the following...
Elijah Liflyand, Akihiko Miyachi (2009)
Studia Mathematica
Similarity:
Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces , 0 < p < 1, on the real line are proved. Two related negative results are also given.
Fabio Nicola (2010)
Studia Mathematica
Similarity:
We study Fourier integral operators of Hörmander’s type acting on the spaces , 1 ≤ p ≤ ∞, of compactly supported distributions whose Fourier transform is in . We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank r of the Hessian of the phase Φ(x,η) with respect to the space variables x. Indeed, we show that operators of order m = -r|1/2-1/p| are bounded on if the mapping is constant on the fibres, of codimension r,...
Romuald Lenczewski (2002)
Studia Mathematica
Similarity:
We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm to the algebra (S) of complex-valued functions on the free semigroup S = FS(z,w) on two generators. First, to given probability measures μ, ν with all moments finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (ℬ,ε,Δ) on two self-adjoint generators X,X’ and a projection P. Then we introduce and study cumulants which are additive under the convolution μ̂* ν̂ = μ̂ ⊗...
Giancarlo Travaglini (1987)
Colloquium Mathematicae
Similarity:
José Bonet, Reinhold Meise (2008)
Studia Mathematica
Similarity:
Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on .
M. Skwarczyński (1991)
Annales Polonici Mathematici
Similarity:
In Sook Park (2005)
Studia Mathematica
Similarity:
Let be a locally compact abelian group and let 1 < p ≤ 2. ’ is the dual group of , and p’ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform if admits a continuous extension . Let denote the collection of such T’s. We show that for any and positive integer n. Moreover, if the factor group of by its identity component is a direct sum of a torsion-free group and a finite group with discrete topology then...
Sergiusz Kęska (2016)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
The purpose of this paper is to analyze the degree of approximation of a function that is a conjugate of a function belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.
Michael Langenbruch (2007)
Studia Mathematica
Similarity:
We characterize the partial differential operators P(D) admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual (Ω̅)-type estimate valid for the bounded holomorphic functions on the characteristic variety near . The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén-Lindelöf-type condition.
Saifallah Ghobber (2015)
Czechoslovak Mathematical Journal
Similarity:
The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg’s uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks’ uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with...
J. J. Guadalupe, V. I. Kolyada (2001)
Studia Mathematica
Similarity:
We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients of -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any the series is the Fourier series of some function φ ∈ ReH¹ with . ...
Rémi Arcangéli, Juan José Torrens (2013)
Studia Mathematica
Similarity:
We collect and extend results on the limit of as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and is the intrinsic seminorm of order l+σ in the Sobolev space . In general, the above limit is equal to , where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.
Abdellatif Chahbi, Brahim Fadli, Samir Kabbaj (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
Let be a compact group, let be a fixed element and let be a continuous automorphism on such that . Using the non-abelian Fourier transform, we determine the non-zero continuous solutions of the functional equation in terms of unitary characters of .
Richard Oberlin, Andreas Seeger, Terence Tao, Christoph Thiele, James Wright (2012)
Journal of the European Mathematical Society
Similarity:
We strengthen the Carleson-Hunt theorem by proving estimates for the -variation of the partial sum operators for Fourier series and integrals, for . Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.
Earl Berkson (2014)
Studia Mathematica
Similarity:
Let , where, for 1 ≤ r < ∞, (resp., ) denotes the class of functions (resp., bounded functions) g: → ℂ such that g has bounded r-variation (resp., uniformly bounded r-variations) on (resp., on the dyadic arcs of ). In the author’s recent article [New York J. Math. 17 (2011)] it was shown that if is a super-reflexive space, and E(·): ℝ → () is the spectral decomposition of a trigonometrically well-bounded operator U ∈ (), then over a suitable non-void open interval of r-values,...
J. P. Schreiber (1971)
Colloquium Mathematicae
Similarity:
Epperson Jay, Frazier Michael
Similarity:
Abstract We develop an almost orthogonal wavelet-type expansion in ℝ² which is adapted to polar coordinates. We start by defining a product Fourier-Hankel transform f̂ and proving a sampling formula for f such that f̂ is compactly supported. For general f, the sampling formula and a partition of unity lead to an identity of the form , in which each function and is concentrated near a certain annular sector, has compactly supported product Fourier-Hankel transform, and is smooth...
W. M. Zajączkowski (2007)
Applicationes Mathematicae
Similarity:
We examine the regularity of solutions to the Stokes system in a neighbourhood of the distinguished axis under the assumptions that the initial velocity v₀ and the external force f belong to some weighted Sobolev spaces. It is assumed that the weight is the (-μ )th power of the distance to the axis. Let , , μ ∈ (0,1). We prove an estimate of the velocity in the norm and of the gradient of the pressure in the norm of . We apply the Fourier transform with respect to the variable along...
V. Karunakaran, R. Roopkumar (2005)
Colloquium Mathematicae
Similarity:
We define various operations on the space of ultra Boehmians like multiplication with certain analytic functions which are Fourier transforms of compactly supported distributions, polynomials, and characters , translation, differentiation. We also prove that the Fourier transform on the space of ultra Boehmians has all the operational properties as in the classical theory.
Brian Fisher, Fatma Al-Sirehy (1999)
Publications de l'Institut Mathématique
Similarity:
Ferenc Móricz (2002)
Studia Mathematica
Similarity:
The harmonic Cesàro operator is defined for a function f in for some 1 ≤ p < ∞ by setting for x > 0 and for x < 0; the harmonic Copson operator ℂ* is defined for a function f in by setting for x ≠ 0. The notation indicates that ℂ and ℂ* are adjoint operators in a certain sense. We present rigorous proofs of the following two commuting relations: (i) If for some 1 ≤ p ≤ 2, then a.e., where f̂ denotes the Fourier transform of f. (ii) If for some 1 < p ≤ 2, then...
T. Godoy, P. Rocha (2013)
Colloquium Mathematicae
Similarity:
We consider the Heisenberg group ℍⁿ = ℂⁿ × ℝ. Let ν be the Borel measure on ℍⁿ defined by , where , w = (w₁,...,wₙ) ∈ ℂⁿ, , and η(w) = η₀(|w|²) with . We characterize the set of pairs (p,q) such that the convolution operator with ν is bounded. We also obtain -improving properties of measures supported on the graph of the function .
Chike Obi (1979)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
Similarity:
Si dimostra che l'equazione considerata nel titolo ammette soluzioni periodiche rappresentabili da una serie di Fourier con un numero finito di termini solo se è lineare.