Adjoints of elliptic cone operators

Juan B. Gil; Gerardo A. Mendoza

doi:10.1353/ajm.2003.0012

Adjoints of elliptic cone operators

Juan B. Gil, Gerardo A. Mendoza

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

We study the adjointness problem for the closed extensions of a general b-elliplic operator A ∈ x^-ν Diff_b^m (M;E), ν > 0, initially defined as an unbounded operator A: C_c^infin; (M;E) ⊃ x^μL_b²(M;E) → x^μL_b²(M;E), μ ∈ ℝ. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.

Original language	English (US)
Pages (from-to)	357-408
Number of pages	52
Journal	American Journal of Mathematics
Volume	125
Issue number	2
DOIs	https://doi.org/10.1353/ajm.2003.0012
State	Published - Apr 2003

All Science Journal Classification (ASJC) codes

General Mathematics

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AB - We study the adjointness problem for the closed extensions of a general b-elliplic operator A ∈ x-ν Diffbm (M;E), ν > 0, initially defined as an unbounded operator A: Ccinfin; (M;E) ⊃ xμLb2(M;E) → xμLb2(M;E), μ ∈ ℝ. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.

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Adjoints of elliptic cone operators

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