Abstract
The linear symmetric systems associated with the modified Cherednik operators and applications
Highlights
Let a be a real Euclidean vector space of dimension d and let R be a root system in a
The original motivation for the study of these operators came from the theory of invariant differential operators: if the triplet (a, R, k) arises from the structure theory of a Riemannian symmetric space of the non-compact type G/K, it is possible to explicitly construct all radial components of the W −invariant differential operators on G/K using the Cherednik operators
The joint spectral theory of Cherednik operators is naturally related to the harmonic analysis on Reimannian symmetric spaces
Summary
Let a be a real Euclidean vector space of dimension d and let R be a root system in a. D, are the modified Cherednik operators, I be an interval of R, (Ap )0≤p≤d a family of functions from I × Rd into the space of m×m matrices with real coefficients ap,i,j (t, x) which are W -invariant with respect to x, symmetric (i.e. ap,i,j (t, x) = ap,j,i (t, x)) and whose all derivatives in x ∈ Rd are bounded and continuous functions of (t, x), the initial data belongs to generalized Sobolev spaces [Hks (Rd )]m and f is a continuous function on an interval I with value in [Hks (Rd )]m. Throughout this paper by C we always represent a positive constant not necessarily the same in each occurrence
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