Results 31 to 40 of about 2,907 (125)
The Bochner–Riesz means for Fourier–Bessel expansions
Journal of Functional Analysis, 2005 The Fourier-Bessel expansion of a sufficiently good function \(f\) on \((0,1)\), for instance, \(f\in C_c^\infty(0,1)\), is given by \[ f(x)\sim \sum^\infty_{j=1}a_j(f) \varphi_j(x),\quad a_j(f):=\int^1_0f(r) \varphi_j(r)\,dr,\tag{*} \] where the orthonormal system \(\{\varphi_j\}\) complete in \(L^2((0,1),dx)\) is defined by means of the Bessel ...
Ciaurri, Óscar, Roncal, Luz
openaire +1 more source
Order-type Henstock and McShane integrals in Banach lattice setting [PDF]
, 2014 We study Henstock-type integrals for functions defined in a compact metric space $T$ endowed with a regular $\sigma$-additive measure $\mu$, and taking values in a Banach lattice $X$.
Candeloro, Domenico +1 more
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On the Rate of Almost Everywhere Convergence of Certain Classical Integral Means [PDF]
, 1999 The main purpose of this article is to establish nearly optimal results concerning the rate of almost everywhere convergence of the Gauss–Weierstrass, Abel–Poisson, and Bochner–Riesz means of the one-dimensional Fourier integral.
Klaas Post +2 more
core +3 more sources
Optimal control of singular Fourier multipliers by maximal operators [PDF]
, 2013 We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de Francia--Semmes,
Bennett, Jonathan
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Fractional Fourier Series on the Torus and Applications
Fractal and FractionalThis paper introduces the fractional Fourier series on the fractional torus and proceeds to investigate several fundamental aspects. Our study includes topics such as fractional convolution, fractional approximation, fractional Fourier inversion, and the
Chen Wang +4 more
doaj +1 more source
L^p-summability of Riesz means for the sublaplacian on complex spheres
, 2008 In this paper we study the L^p-convergence of the Riesz means for the sublaplacian on the sphere S^{2n-1} in the complex n-dimensional space C^n. We show that the Riesz means of order delta of a function f converge to f in L^p(S^{2n-1}) when delta>delta ...
Casarino, Valentina, Peloso, Marco M.
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Duality for Evolutionary Equations With Applications to Null Controllability
Mathematical Methods in the Applied Sciences, Volume 49, Issue 5, Page 4144-4166, 30 March 2026.ABSTRACT We study evolutionary equations in exponentially weighted L2$$ {\mathrm{L}}^2 $$‐spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the ν$$ \nu $$‐adjoint system, which turns out to describe a system backwards in time. We prove well‐posedness for the ν$$ \nu $$‐adjoint system. We then apply
Andreas Buchinger, Christian Seifert
wiley +1 more source
The weak (1,1) boundedness of Fourier integral operators with complex phases
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let T$T$ be a Fourier integral operator of order −(n−1)/2$-(n-1)/2$ associated with a canonical relation locally parametrised by a real‐phase function. A fundamental result due to Seeger, Sogge and Stein proved in the 90's gives the boundedness of T$T$ from the Hardy space H1$H^1$ into L1$L^1$. Additionally, it was shown by T.
Duván Cardona, Michael Ruzhansky
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A Choquet theory of Lipschitz‐free spaces
Proceedings of the London Mathematical Society, Volume 132, Issue 2, February 2026.Abstract Let (M,d)$(M,d)$ be a complete metric space and let F(M)$\mathcal {F}({M})$ denote the Lipschitz‐free space over M$M$. We develop a ‘Choquet theory of Lipschitz‐free spaces’ that draws from the classical Choquet theory and the De Leeuw representation of elements of F(M)$\mathcal {F}({M})$ (and its bi‐dual) by positive Radon measures on βM ...
Richard J. Smith
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Mathematische Nachrichten, Volume 298, Issue 8, Page 2499-2546, August 2025.Abstract In this paper, the approximation of Dirac operators with general δ$\delta$‐shell potentials supported on C2$C^2$‐curves in R2$\mathbb {R}^2$ or C2$C^2$‐surfaces in R3$\mathbb {R}^3$, which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the δ$\delta$‐interaction that a family of Dirac operators ...
Jussi Behrndt +2 more
wiley +1 more source