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Operators of Hadamard type on spaces of smooth functions
Author(s) -
Vogt Dietmar
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300269
Subject(s) - mathematics , hadamard transform , monomial , algebra over a field , unit sphere , eigenvalues and eigenvectors , type (biology) , pure mathematics , operator theory , unit (ring theory) , discrete mathematics , mathematical analysis , mathematics education , ecology , biology , physics , quantum mechanics
For an open set Ω ⊂ R dwe study the algebra M ( Ω ) of continuous linear operators onC ∞ ( Ω )admitting the monomials as eigenvectors. We give a concrete representation of these operators and evaluate it explicitly for the unit ball and the whole of R d . We also study the topology of M ( Ω ) and the algebra of eigenvalue sequences.