zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Weak Bloch property and weight estimates for elliptic operators. Appendix: On the equality between weak and strong extensions (by M. A. Shubin and J. Sjöstrand). (English) Zbl 0716.35052
Sémin. Équations Dériv. Partielles 1989-1990, No.5, 30 p. (1990).

The paper deals with the following problem.

Let A denote a differential operator on a non-compact Riemannian manifold M, and assume that A defines an unbounded operator in the Hilbert space L 2 (M). Assume that for some complex λ we know a solution u of the equation Au=λu, when can we conclude that λ is in the spectrum σ (A) of the operator A in L 2 (M)? After an introduction with the main definitions and some preliminary lemmata, one considers weight estimates and decay of Green functions; then the third section deals with uniform properly supported pseudo-differential operators and structural inverse operators; and the last section contains some results related to the spectral properties of uniformly elliptic operators on manifolds of subexponential growth.

Reviewer: G.Jumarie
MSC:
35P05General topics in linear spectral theory of PDE
35J15Second order elliptic equations, general
35S05General theory of pseudodifferential operators