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Some L p analogues of Weyl's theorem of invariability
Author(s) -
Osipov Andrey
Publication year - 2007
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.200410505
Subject(s) - mathematics , order (exchange) , differential equation , space (punctuation) , pure mathematics , differential operator , mathematical physics , mathematical analysis , combinatorics , linguistics , philosophy , finance , economics
A well‐known result on Sturm–Liouville operators due to H. Weyl states that the property of all solutions of the equation ‐( p ( x ) y ′)′ + q ( x ) y = λy, x ≥ 0, λ ∈ ℂ, to be in L 2 [0, ∞) is invariable with respect to the value of λ . Here we obtain some extensions of this theorem with the second order differential equation replaced by a quasi‐differential equation of an arbitrary order and the space L 2 replaced by L p , 1 ≤ p ≤ ∞. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)