Pseudodifferential Operators Associated with a Semigroup of Operators

Pseudodifferential operators associated with a semigroup of operators

Pseudodifferential Operators

The study of pseudodifferential operators emerged in the 1960’s, having its origins in the study of singular integro-differential operators. In fact, Friedrichs and Lax coined the term “pseudodifferential operator” in their 1965 paper entitled “Boundary Value Problems for First Order Operators”. Since that time, pseudodifferential operators have proved useful in many arenas of modern analysis a...

Pseudodifferential operators with homogeneous symbols

We prove boundedness of pseudodifferential operators with symbols satisfying the conditions |∂ ξ ∂ xa(x, ξ)| ≤ Cβ,γ |ξ|m−|β|+|γ| on homogeneous Besov-Lipschitz and Triebel-Lizorkin spaces

Pseudodifferential Operators with Rough Symbols

In this work, we develop L boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the x variable. Moreover, the B(L) operator norms are estimated explicitly in terms of scale invariant quantities involving the symbols. All the estimates are shown to be sharp with respect to the required smoothness in the ξ variable. As a corollary, we obtain L...

Integral Operators, Pseudodifferential Operators, and Gabor Frames

This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...