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Estimates of Eigenfunctions for One Class of Boundary Conditions
Author(s) -
Minkin A.,
Shuster L.
Publication year - 1997
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/s0024609396002573
Subject(s) - eigenfunction , mathematics , differential operator , spectrum (functional analysis) , operator (biology) , boundary (topology) , class (philosophy) , mathematics subject classification , boundary value problem , order (exchange) , ordinary differential equation , combinatorics , mathematical analysis , pure mathematics , eigenvalues and eigenvectors , differential equation , physics , quantum mechanics , chemistry , biochemistry , finance , repressor , artificial intelligence , computer science , transcription factor , economics , gene
Requirements for boundary conditions are found which imply sharp by order estimates in L ∞ ‐metrics of eigenfunctions of the ordinary differential operator l ( y ) = D n y + Σ k = 0 n − 2p n − k( x ) D k y , p n − k( x ) ∈ L 1 ( − 1 , 1 ) ; D = 1 i d d x , x ∈ [ − 1 , 1 ] .It is shown that the inequalities‖ y λ ( k )‖ ∞ ⩽ c∣ λ ∣k / n‖ y λ ‖ 2 , c = const .for the eigenfunctions { y λ } yield certain restrictions on the spectrum. 1991 Mathematics Subject Classification 34L05.