scholarly journals On the positive semigroups generated by Fleming-Viot type differential operators

2019 ◽  
Vol 18 (1) ◽  
pp. 323-340 ◽  
Author(s):  
Francesco Altomare ◽  
◽  
Mirella Cappelletti Montano ◽  
Vita Leonessa ◽  
Keyword(s):  
Differential Operators ◽  
Positive Semigroups

scholarly journals Positive Semigroups Generated by Degenerate Second-Order Differential Operators

2008 ◽  
Vol 51 (3) ◽  
pp. 431-458
Author(s):  
Francesco Altomare ◽  
Graziana Musceo
Keyword(s):  
Differential Operators ◽  
Second Order ◽  
Positive Semigroups

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

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