@inbook{210e90e446ad459489812d89d517451b,

title = "Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets",

abstract = "This paper is a continuation of [8] in the direction of proving the conjecture that the spherical transform on a nilpotent Gelfand pair (N, K) establishes an isomorphism between the space of K-invariant Schwartz functions on N and the space of Schwartz functions restricted to the Gelfand spectrum ΣD, appropriately embedded in a Euclidean space. We prove a result, of independent interest for the representation-theoretical problems that are involved, which can be viewed as a generalised Hadamard lemma for K-invariant functions on N. The context is that of nilpotent Gelfand pairs satisfying Vinberg's condition. This means that the Lie algebra n of N (which is step 2) decomposes as v ⊕ [n,n] with v irreducible under K.",

keywords = "Gelfand pairs, Invariants, Schwartz functions, Spherical transform",

author = "V{\'e}ronique Fischer and Fulvio Ricci and Oksana Yakimova",

year = "2013",

month = jan,

day = "1",

doi = "10.1007/978-1-4614-7193-6_5",

language = "English",

isbn = "9781461471929",

series = "Progress in Mathematics",

publisher = "Birkhauser Boston",

pages = "81--112",

editor = "A. Huckleberry and I. Penkov and G. Zuckerman",

booktitle = "Lie Groups",

address = "USA United States",

}