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On univariate fractional calculus with general bivariate analytic kernels
Several fractional integral and derivative operators have been defined recently with a bivariate structure, acting on functions of a single variable...
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On fractional calculus with analytic kernels with respect to functions
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified...
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Paired Kernels and Their Applications
This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space
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A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels
We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure...
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A Note on ξ-Bergman Kernels
In the present note, we introduce the ξ -complex singularity exponents, which come from the asymptotic property of ξ -Bergman kernels on sub-level sets...
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Nuclearity for power series kernels in higher dimensions
In this work we establish the nuclearity on Lebesgue spaces for a class of power series kernels in higher dimensions. This class includes important...
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Dynamical Systems of p-Bergman Kernels
In this paper, we consider the dynamical system of p-Bergman kernels. This is useful when we consider a projective manifold with intermediate Kodaira...
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Totally positive kernels, Pólya frequency functions, and their transforms
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes....
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Gaussian limit for determinantal point processes with J-Hermitian kernels
We show that the central limit theorem for linear statistics over determinantal point processes with J-Hermitian kernels holds under fairly general...
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Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators
Cauchy–de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and...
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Functionals with extrema at reproducing kernels
We show that certain monotone functionals on the Hardy spaces and convex functionals on the Bergman spaces are maximized at the normalized...
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The characteristic function of Gaussian stochastic volatility models: an analytic expression
Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylised facts of...
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Comparison principles for a class of general integro-differential inequalities with applications
Comparison principles for fractional differential equations have been investigated in many papers using different types of fractional integral and...