Degenerate differential equations and modified Szász-Mirakjan operators
type: Item
instance of: scholarly article
title: Degenerate differential equations and modified Szász-Mirakjan operators
zbMATH Open document ID: 1231.47035
author: Francesco Altomare
author: Sabina Milella
publication date: 2010-10-14T00:00:00Z
review text: This paper deals with operators \(L\) defined by \[ (Lu)(x) = xu'' (x) + \beta(x)u' (x) + \tau(x)u(x),\quad x \in [0, \infty]. \] Conditions are sought under which this operator generates a \(C_0\)-semigroup. Various weighted spaces of continuous functions for the domain of \(L\) are considered, as are Wentzell-type boundary conditions. The authors prove several semigroup generation theorems under a variety of assumptions. The paper is particularly useful for the reader who is interested in semigroup generation by singular differential operators.
reviewed by: J. W. Neuberger
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 5800239
zbMATH Keywords: positive semigroup
zbMATH Keywords: parabolic equation
zbMATH Keywords: weighted continuous function space
zbMATH Keywords: approximation by positive operators
MaRDI profile type: Publication
full work available at URL: s12215-010-0017-z
OpenAlex ID: W2009567487
cites work: APPROXIMATION BY POSITIVE OPERATORS OF THE C0–SEMIGROUPS ASSOCIATED WITH ONE-DIMENSIONAL DIFFUSION EQUATIONS: PART I
cites work: Degenerate evolution equations in weighted continuous function spaces, Markov processes and the Black--Scholes equation. I.
cites work: Degenerate evolution equations in weighted continuous function spaces, Markov processes and the Black--Scholes equation. II.
cites work: On some degenerate differential operators on weighted function spaces
cites work: Q3400210
cites work: Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum
cites work: Shape preserving properties of some positive linear operators on unbounded intervals
cites work: Q4441406
cites work: Q4727718
cites work: Q3469775
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: The parabolic differential equations and the associated semigroups of transformation
cites work: Multi-dimensional diffusion and the Markov process on the boundary
cites work: Q4040288
cites work: Approximation of semi-groups of operators
DOI: 10.1007/S12215-010-0017-Z
Recommended article: On a degenerate differential-operator equation
Recommended article: Q5012934
Recommended article: Degenerate differential-operator equations of higher order and arbitrary weight
Recommended article: Degenerate differential operators with parameters
Recommended article: On the Solvability of Certain Degenerate Partial Differential Operators
Recommended article: On Degenerate Partial Differential Equations
Recommended article: Q2939005
Recommended article: Singular Degenerate Differential Operators and Applications
Recommended article: Degenerate differential-operator equations on infinite intervals
Recommended article: Q5219123
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 5800239