Fréchet Algebra Techniques for Boundary Value Problems on Noncompact Manifolds: Fredholm Criteria and Functional Calculus via Spectral Invariance | Zendy

Schrohe Elmar | Zendy

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Fréchet Algebra Techniques for Boundary Value Problems on Noncompact Manifolds: Fredholm Criteria and Functional Calculus via Spectral Invariance

Author(s) -

Schrohe Elmar

Publication year - 1999

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.19991990108

Subject(s) - mathematics , functional calculus , hilbert space , holomorphic functional calculus , invariant (physics) , sobolev space , pure mathematics , modulo , subalgebra , holomorphic function , algebra over a field , banach space , discrete mathematics , approximation property , mathematical physics

A Boutet de Monvel type calculus is developed for boundary value problems on (possibly) noncompact manifolds. It is based on a class of weighted symbols and Sobolev spaces. If the underlying manifold is compact, one recovers the standard calculus. The following is proven: 1 The algebra G of Green operators of order and type zero is a spectrally invariant Fréchet subalgebra of L (H), H a suitable Hilbert space, i. e.,2 Focusing on the elements of order and type zero is no restriction since there are order reducing operators within the calculus. 3 There is a necessary and sufficient criterion for the Fredholm property of boundary value problems, based on the invertibility of symbols modulo lower order symbols, and 4 There is a holomorphic functional calculus for the elements of G in several complex variables.

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