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Critical Numbers for Poisson and Heat Semigroups
In this chapter, we show that the critical numbers are intrinsic in the sense that we could have equivalently defined them through other families of...
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Discrete Hölder spaces and their characterization via semigroups associated with the discrete Laplacian and kernel estimates
In this paper, we characterize the discrete Hölder spaces by means of the heat and Poisson semigroups associated with the discrete Laplacian. These...
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Function spaces via fractional Poisson kernel on Carnot groups and applications
We provide a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel and Poisson kernel. We...
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Quantitative estimates for bounded holomorphic semigroups
We revisit the theory of one-parameter semigroups of linear operators on Banach spaces in order to prove quantitative bounds for bounded holomorphic...
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Dirichlet Problem on the Half-Line for an Abstract Euler–Poisson–Darboux Equation Containing Powers of an Unbounded Operator
AbstractWe consider an abstract Euler–Poisson–Darboux equation containing powers of an unbounded operator that is the generator of a Bessel operator...
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Green’s Function and the Pointwise Behaviors of the Vlasov-Poisson-Fokker-Planck System
The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in three...
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Boundedness of the differential transforms for the generalized Poisson operators generated by Laplacian
In this paper, we consider the boundedness of the differential transforms for the generalized Poisson operators associated with the Laplace operator
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Markov Processes, Transition Functions and Feller Semigroups
In this chapterMarkov process Transition function Feller semigroup we introduce a class of (temporally homogeneous) Markov processes which we will...
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The Heat Flow in Random Walk Spaces
This chapter focuses on the study of the heat flow in random walk spaces.
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Further Theorems Inspired by Ambartsumian
We continue to derive results in the spirit of classical Ambartsumian Theorem 14.1 . In the first part we...
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Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds
This note is concerned with two families of operators related to the fractional Laplacian, the first arising from the Caffarelli-Silvestre extension...
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A map** property of the heat volume potential
We consider the volume potential associated with the heat operator and we prove a map** property in the space of distributions which are the time...
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Exact Splitting Methods for Semigroups Generated by Inhomogeneous Quadratic Differential Operators
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential...
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Noncommutative analysis of Hermite expansions
This paper is devoted to the study of semi-commutative harmonic analysis associated with Hermite semigroups. In the first part, we establish the...