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Wild Spectral Behaviour of Anharmonic Oscillators
Author(s) -
Davies E. B.
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609300007050
Subject(s) - mathematics , bounded function , mathematics subject classification , anharmonicity , banach space , ordinary differential equation , pure mathematics , sequence (biology) , mathematical analysis , differential equation , quantum mechanics , physics , biology , genetics
We show that the norms of the sequence of spectral projections of certain non‐self‐adjoint ordinary differential operators cannot be polynomially bounded. The proof involves the investigation of ‘tame’ bi‐orthogonal systems in Banach spaces. 2000 Mathematics Subject Classification 34L10, 46B15.