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On One Integral Representation of Solutions of Polyharmonic Equation
AbstractIn the paper, an elementary solution of polyharmonic equation is determined and, with the help of it, an integral representation of solutions...
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Integral Representation of the Mittag-Leffler Function
AbstractIn this paper, we obtain a generalization of the integral representation of the gamma function, which shows that the Hankel contour allows...
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An Integral Representation for Inverse Moments
Inverse moments of discrete random variables are traditionally expressed by summations. But summations are often difficult to simplify. In this note,...
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On an Analytical Representation of an Integral Related to the Fock Integral Appearing in the Calculations of the Electromagnetic Fields of Dipole Sources at the Interface between Two Half-Spaces
AbstractThe Fock integral is called after Fock who introduced it to theoretically analyze the electromagnetic field of magnetic dipoles at the...
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Spectral decomposition of Dunkl Laplacian and application to a radial integral representation for the Dunkl kernel
For the Dunkl Laplacian associated with a Coxeter group, the Von Neumann spectral decomposition is given. As a consequence, for the Dunkl kernel an...
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Integral Equations and Integral Transforms
This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of...
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A Compactness and Integral-Representation Result
The main result of this chapter is a compactness and integral-representation result for the Γ-limits of the families {Fε(⋅, A)}ε, which we can obtain...
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Solution of the Interpretation Tomography Problem in Geophysics under the Linear Integral Representation Method and Theories of Discrete Gravity and the Magnetic Potential
AbstractA fundamentally new approach to solving inverse problems in geophysics based on the linear integral representation method and the theories of...
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Wavelet representation of singular integral operators
This article develops a novel approach to the representation of singular integral operators of Calderón–Zygmund type in terms of continuous model...
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On the Integral Representation and the Raşa, Jensen and Hermite–Hadamard Inequalities for Box-Convex Functions
We give the integral representation of Popoviciu’s (Mathematica 8:1–85, 1934) box-( m , n )-convex functions. Based on this integral representation, we...
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Representation of Weierstrass integral via Poisson integrals
In our research, we have presented a second-order linear partial differential equation in polar coordinates. Considering this differential equation...
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Theory of Classical Gaseous Polytropes in an Integral Representation. I. Some General Results
The well known results of the theory of classical gaseous polytropes are presented in the framework of an integral approach where the standard...
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Analytical Representation of the Integral Scattering Cross-Section in the Integrofunctional Discrete Source Method
AbstractAn analytical expression is obtained for the total scattering cross-section in the discrete source method, which uses the representation of...
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An integral equation representation for American better-of option on two underlying assets
In this paper, we study the problem for pricing of American better-of option on two assets. Due to two correlated underlying assets and...
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Integral representation and computational properties of the incomplete Fox–Wright function
The main focus of this paper is to investigate some new properties of the incomplete Fox–Wright function. We derive an integral representation of the...
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Learning integral operators via neural integral equations
Nonlinear operators with long-distance spatiotemporal dependencies are fundamental in modelling complex systems across sciences; yet, learning these...
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Numerical Construction of the Transform of the Kernel of the Integral Representation of the Poincaré–Steklov Operator for an Elastic Strip
AbstractFor an isotropic stratified elastic strip we consider the Poincaré–Steklov operator that maps normal stresses into normal displacements on...
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Dynamical actions and q-representation theory for double-scaled SYK
We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on the quantum group SU q (1 , 1). We...
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On the evaluation of the Ray-Singer torsion path integral
There are very few explicit evaluations of path integrals for topological gauge theories in more than 3 dimensions. Here we provide such a...