Weyl's spectral asymptotics formula for nonelliptic operators of the Dirichlet problem

Journal Article · Fri Oct 10 04:00:00 EDT 1986 · J. Sov. Math.; (United States)

DOI:https://doi.org/10.1007/BF01104864· OSTI ID:5660673

Andreev, A S

One considers the asymptotic behavior of the spectrum of the Dirichlet problem for a class of operators with constant coefficients, including in it the hypoelliptic operators. For this class one obtains the classical Weyl formula of spectral asymptotics. The residual of the distribution function of the spectrum is estimated in terms of the measure of the interior boundary layer of the level surface of the operator symbol. These results can be carried over also to the vectorial case. One considers separately the class of operators whose quadratic form corresponds to the differential norm of the Sobolev type. For the indicated class one describes all possible elementary generalizations of the Weyl formula.

• OSTI ID: 5660673
• Journal Information: J. Sov. Math.; (United States), Journal Name: J. Sov. Math.; (United States) Vol. 35:1; ISSN JSOMA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
BOUNDARY LAYERS
DIRICHLET PROBLEM
DISTRIBUTION FUNCTIONS
EUCLIDEAN SPACE
FIELD THEORIES
FUNCTIONS
LAYERS
MATHEMATICAL MANIFOLDS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
RIEMANN SPACE
SPACE
SPECTRA
UNIFIED-FIELD THEORIES
WEYL UNIFIED THEORY