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On Poisson Semigroup Hypercontractivity for Higher-Dimensional Spheres
AbstractIn this note we consider a variant of a question of Mueller and Weissler raised in 1982, thereby complementing a classical result of Beckner...
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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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Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform
The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with...
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Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps
This paper aims to investigate stochastic fractional Schrödinger evolution equations with potential and Poisson jumps in Hilbert space. The...
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Approximate Controllability for Hilfer Fractional Stochastic Non-instantaneous Impulsive Differential System with Rosenblatt Process and Poisson Jumps
This paper discusses the approximate controllability of Hilfer fractional stochastic differential system involving non-instantaneous impulses with...
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Semigroup Theory and Markov Processes
To construct a discrete parameter homogeneous Markov process with state space (...
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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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Stochastic Dirichlet–Poisson Problem on Hilbert Spaces
This paper is devoted to the study of the existence and the uniqueness of the solution of the Stochastic Dirichlet-Poisson problems on Hilbert...
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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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Trajectory Controllability of Hilfer Fractional Neutral Stochastic Differential Equations with Deviated Argument Using Rosenblatt Process and Poisson Jumps
The theoretical approach of Trajectory(T-)controllability of Hilfer fractional neutral stochastic differential equation with deviated arguments,...
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Existence of a Class of Doubly Perturbed Stochastic Functional Differential Equations with Poisson Jumps
In this paper, we use successive approximations and Picard iterative method to establish the existence and uniqueness of mild solution for a class of...
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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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Convergence from the Two-Species Vlasov-Poisson-Boltzmann System to the Two-Fluid Incompressible Navier-Stokes-Fourier-Poisson System with Ohm’s Law
In this paper, we justify the convergence from the two-species Vlasov-Poisson-Boltzmann (VPB, for short) system to the two-fluid incompressible...
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Existence of Optimal Control for a Class of Kirchhoff–Poisson System
We discuss an optimal control problem for the Kirchhoff–Poisson type controlled system. By using variational methods and embedding theorem, we obtain...
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Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by fBm with Noncompact Semigroup via Mönch Fixed Point
The aim of this work is to study the mild solutions for a class of impulsive neutral stochastic functional integrodifferential equations driven by...
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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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Large Time Behavior of the 1D Isentropic Navier-Stokes-Poisson System
The initial value problem (IVP) for the one-dimensional isentropic compressible Navier-Stokes-Poisson (CNSP) system is considered in this paper. For...
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The convergence rate of truncated hypersingular integrals generated by the modified Poisson semigroup
Hypersingular integrals have appeared as effective tools for inversion of multidimensional potential-type operators such as Riesz, Bessel, Flett,...
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On the Solvability of Initial Problems for an Abstract Generalized Euler–Poisson–Darboux Equation of Higher Order
AbstractUsing integral representations of Poisson type, it is established in the paper that the Cauchy problem for a number of abstract higher order...