Convolution Equations in Certain Banach Spaces

DOI10.2307/2048413zbMath0748.46017OpenAlexW4235362198MaRDI QIDQ3971107

Alexander L. Koldobsky

Publication date: 25 June 1992

Full work available at URL: https://doi.org/10.2307/2048413

zbMATH Keywords

potentialFourier transforminverse problemconvolution equationsfinite Borel measureinfinite- dimensional Hilbert spacesFourier transform of norms in some finite dimensional-spacesisometric embedding into \(L_ p\)-spacelimit correlations

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Equations and inequalities involving linear operators, with vector unknowns (47A50) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Measures and integration on abstract linear spaces (46G12) Probability theory on linear topological spaces (60B11)

Related Items

On a question of Pietsch ⋮ Fourier transform and convolution in the space \(\ell_ 1\) ⋮ The Fourier transform technique for convolution equations in the infinite dimensional \(\ell_ q\)-spaces ⋮ Characterization of measures by potentials

Cites Work

• Uniqueness theorems for measures in \(L_ r\) and \(C_ o(\Omega)\)
• Representation of \(L_ p\)-norms and isometric embedding in \(L_ p\)- spaces
• Moments of measures on Banach spaces
• Potential operators and equimeasurability
• The L p Norm of Sums of Translates of a Function
• Certain Integral Equalities which Imply Equimeasurability of Functions
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