2 4 O ct 2 00 9 WEYL GROUP INVARIANTS AND APPLICATION TO SPHERICAL HARMONIC ANALYSIS ON SYMMETRIC SPACES
نویسنده
چکیده
Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/injective limits, specifically to theorems of Paley–Wiener type.
منابع مشابه
Weyl Group Invariants and Application to Spherical Harmonic Analysis on Symmetric Spaces
Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/in...
متن کاملar X iv : m at h / 02 10 17 4 v 1 [ m at h . G T ] 1 1 O ct 2 00 2 GENERATING FUNCTIONS , FIBONACCI NUMBERS AND RATIONAL KNOTS
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numbers occur in the enumeration of fibered achiral and unknotting number one rat...
متن کاملar X iv : m at h / 06 06 65 4 v 2 [ m at h . A T ] 1 6 O ct 2 00 6 EULER CHARACTERISTICS OF ALGEBRAIC VARIETIES
The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodge-theoretic invariants of algebraic varieties were announced by the first and third authors in [4, 11].
متن کاملar X iv : 0 81 0 . 30 28 v 1 [ m at h . G N ] 1 6 O ct 2 00 8 OSCILLATOR TOPOLOGIES ON A PARATOPOLOGICAL GROUP AND RELATED NUMBER INVARIANTS
We introduce and study oscillator topologies on paratopological groups and define certain related number invariants. As an application we prove that a Hausdorff paratopological group G admits a weaker Hausdorff group topology provided G is 3-oscillating. A paratopological group G is 3-oscillating (resp. 2-oscillating) provided for any neighborhood U of the unity e of G there is a neighborhood V...
متن کاملm at h . FA ] 1 2 O ct 2 00 6 EQUIVALENCE OF QUOTIENT HILBERT MODULES – II RONALD
For any open, connected and bounded set Ω ⊆ C m , let A be a natural function algebra consisting of functions holomorphic on Ω. Let M be a Hilbert module over the algebra A and M0 ⊆ M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module Q = M ⊖ M0 in the case of k = 2...
متن کامل