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Integrability Properties of Integral Transforms Via Morrey Spaces
We show that integrability properties of integral transforms with kernel depending on the product of arguments (which include in particular, popular...
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Spectral Theorems Associated with the Riemann–Liouville Two-Wavelet Localization Operators
In this paper, we prove the boundedness and compactness of localization operators associated with Riemann–Liouville wavelet transforms, which depend...
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A generalization of the Paley–Wiener theorem for Mellin transforms and metric characterization of function spaces
We characterize the function space whose elements have a Mellin transform with exponential decay at infinity. This result can be seen as a...
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Time–frequency Analysis Associated with Some Partial Differential Operators
In this paper, we prove the boundedness and compactness of localization operators associated with Riemann–Liouville wavelet transforms, which depend...
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Fractal zeta functions and complex dimensions of relative fractal drums
The theory of “zeta functions of fractal strings” has been initiated by the first author in the early 1990s and developed jointly with his...
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Operator Invariance
Linear time invariant (LTI) systems have produced a rich set of ideas including the concepts of convolution, impulse response function, causality,...
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The Riemann ζ function and asymptotics for Stieltjes fractions
We study the asymptotic behaviour of the coefficients in the continued fractions corresponding to Stieltjes transforms of weight functions on a...
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Ultradistributions and Time-Frequency Analysis
The aim of the paper is to show the connection between the theory of ultradistributions and time-frequency analysis. This is done through...
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Integral Transforms Controlled by Maximal Functions
The paper characterizes the kernel functions on ℝn with the property that the associated convolution operators are controlled by certain maximal...
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Some General Approximation Error and Convergence Rate Estimates in Statistical Learning Theory
In statistical learning theory, reproducing kernel Hilbert spaces are used basically as the hypothese space in the approximation of the regression...
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The Calderón reproducing formula, windowed X-ray transforms, and radon transforms in LP-spaces
The generalized Calderón reproducing formula involving “wavelet measure” is established for functions f ∈ L p (ℝ n ). The special choice of the wavelet...
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