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Radon–Kipriyanov Transform of Laplace Series by Weight Spherical Functions
AbstractIn this paper we consider the Radon–Kipriyanov transform and its relationship with the special Radon transform. The representation of plane...
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Existence and asymptotic behavior of Radon measure-valued solutions for a class of nonlinear parabolic equations
In this paper we address the weak Radon measure-valued solutions associated with the Young measure for a class of nonlinear parabolic equations with...
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Radon Measure Solutions to Riemann Problems for Isentropic Compressible Euler Equations of Polytropic Gases
We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures, and the solutions admit...
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The Radon-Carleman Problem
In view of the pioneering work and fundamental contributions of Johann Karl August Radon and Torsten Carleman, we find it appropriate to label the...
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Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions
We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ d with d ≥ 1 and show that, even when they start at some...
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Abstract Measure Theory
The objective of this chapter is to extend measure theory by generalizing the concept of measure to include more general sets other than sets in...
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The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
We prove a version of the Lebesgue differentiation theorem for map**s that are defined on a measure space and take values into a metric space, with...
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General Measure and Integration
The first five sections of this chapter are dedicated to the study of measure theory, measurable functions on a measure space, general integration...
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Inequalities for the derivatives of the Radon transform on convex bodies
It was proved in [22] that the sup-norm of the Radon transform of an arbitrary probability density on an origin-symmetric convex body of volume 1 is...
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Measure Theoretical and Topological Rudiments
The material in this chapter is centered around the notions of measure and topology, including sigma-algebras, Borelians, ordinary measures, outer...
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Quaternionic Monge–Ampère Measure on Pluripolar Set
In this paper, we prove that in a hyperconvex domain Ω in ℍ n , if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure,...
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Lebesgue type decompositions and Radon–Nikodym derivatives for pairs of bounded linear operators
For a pair of bounded linear Hilbert space operators A and B one considers the Lebesgue type decompositions of B with respect to A into an almost...
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A level line of the Gaussian free field with measure-valued boundary conditions
In this article, we construct samples of Schramm-Loewner-evolution-like curves out of samples of the conformal loop ensemble and Poisson point...
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Support theorems for Funk-type isodistant Radon transforms on constant curvature spaces
A connected maximal submanifold in a constant curvature space is called isodistant if its points are in equal distances from a totally geodesic of...
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Completion Procedures in Measure Theory
We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null...