Pseudo-differential operators and Markov semigroups on compact Lie groups
نویسندگان
چکیده
منابع مشابه
-bounds for Pseudo-differential Operators on Compact Lie Groups
Given a compact Lie group G, in this paper we establish L p-bounds for pseudo-differential operators in L p(G). The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space G× Ĝ, where Ĝ is the unitary dual of G. We obtain two different types of L p bounds: first for finite regularity symbols and second for smooth symbols. The c...
متن کاملInvariant Differential Operators for Non-Compact Lie Groups: Parabolic Subalgebras
In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients the cuspidal parabolic subalgebras. We explicate also the maximal parabolic subalgebras, since these are also important even when they are not cuspidal. Our approach is easily generalised to the supersymmetric and quantum group sett...
متن کاملMarkov Semigroups and Groups of Operators
We consider different realizations of the operators Lθ,a u(x) := xu(x) + (ax + θx)u(x), θ ∈ R, a ∈ R, acting on suitable spaces of real valued continuous functions. The main results deal with the existence of Feller semigroups generated by Lθ,a and the representation Lθ,a = G 2 a + θGa, where Gau = xu, 0 ≤ a ≤ 1, generates a (not necessarily strongly continuous) group. Explicit formulas of the ...
متن کاملDifferential Invariant Algebras of Lie Pseudo–Groups
The goal of this paper is to describe, in as much detail as possible, the structure of the algebra of differential invariants of a Lie pseudo-group. Under the assumption of local freeness of the prolonged pseudo-group action, we develop algorithms for locating a finite generating set of differential invariants, establishing the recurrence relations for the differentiated invariants, and fixing ...
متن کاملDifferential Invariants for Lie Pseudo-groups
Lie pseudo-groups, roughly speaking, are the infinite-dimensional counterparts of local Lie groups of transformations. Pseudo-groups were first studied systematically at the end of the 19th century by Sophus Lie, whose great insight in the subject was to postulate the additional condition that pseudo-group transformations form the general solution to a system of partial differential equations, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.05.067