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A Characterization of Fredholm Pseudo‐Differential Operators
Author(s) -
Fan Qihong,
Wong M. W.
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610796004632
Subject(s) - sobolev space , differential operator , mathematics , characterization (materials science) , differential (mechanical device) , fredholm theory , pseudo differential operator , elliptic operator , extension (predicate logic) , fredholm integral equation , domain (mathematical analysis) , parametrix , order (exchange) , operator (biology) , pure mathematics , fredholm operator , space (punctuation) , mathematical analysis , compact operator , semi elliptic operator , physics , computer science , hypoelliptic operator , integral equation , repressor , chemistry , optics , operating system , biochemistry , transcription factor , thermodynamics , programming language , finance , economics , gene
We give a necessary and sufficient condition on an elliptic symbol σ of order m to ensure that the unique closed extension in L p (ℝ n ) for 1 < p < ∞, of the pseudo‐differential operator T σ , initially defined on the Schwartz space, is a Fredholm operator from L p (ℝ n ) into L p (ℝ n ) with domain H m , p , where H m , p is the L p Sobolev space of order m .