Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. BEALS: A general calculus of pseudodifferential operators. Duke Math. J. 42, 1–42 (1975)
K. Kh. BOITMATOV, A.G. KOSTYUCHENKO: The distribution of the eigenvalues of the equation Au=λBu in the whole space. Soviet Math. Dokl. 30 (1) 245–248 (1984)
M.S. BIRMAN, M.Z. SOLOMJAK: Asymptotics of the spectrum of pseudodifferential operators with anisotropic-homogeneous symbols. Vestnik Leningrad Univ. Math. 10 (1982) 237–247 et 12 (1980) 155–161
M.S. BIRMAN, M.Z. SOLOMJAK: Compact operators whose singular numbers have powerlike asymptotics. J. Soviet Math. 27 (1) (1984) 2442–2447
M.S. BIRMAN, M.Z. SOLOMJAK: Asymptotic behavior of the spectrum of differential equations. J. Soviet Math. 12 (3) (1979) 247–283
Y. COLIN DE VERDIERE: Une formule de trace pour l'opérateur de Schrödinger dans R 3. Ann. E.N.S. 14 (1) 27–39 (1981).
M. DAUGE, D. ROBERT: Formule de Weyl pour une classe d'opérateurs pseudodifférentiels d'ordre négatif sur L2(R n). Note C.R. Acad. Sc. Paris 302 Série I, (5) 175–178 (1986)
V.I. FEIGIN: Sharp estimates of the remainder in the spectral asymptotic for pseudodifferential operators in R n. Funk. Anal. Ego Prilozheniya. 16 (3), 88–89 (1982)
J. FLECKINGER, M.L. LAPIDUS: Eigenvalues of elliptic boundary value problems with an indefinite weight function. Preprint May 1985
I.C. GOHBERG, M.G. KREIN: Introduction à la théorie des opérateurs linéaires non autoadjoints. Dunod (1972)
G. GRUBB: Singular Green operators and their spectral asymptotics. Duke Math. J. 51 (3) (1984) 477–528
L. GUILLOPE: Une formule de trace pour l'opérateur de Schrödinger dans R n. Thèse de 3ème cycle. Univ. de Grenoble (1981)
B. HELFFER, D. ROBERT: Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles. Journal of Functional Analysis 53 (3) (1983) 246–268
B. HELFFER, D. ROBERT: Propriétés asymptotiques du spectre d'opérateurs pseudodifférentiels sur R n. Comm. in Partial Differential Equations 7 (7) 795–882 (1982)
L. HÖRMANDER: The Weyl Calculus of pseudodifferential operators. CPAM 32, 359–443 (1979)
L. HÖRMANDER: On the asymptotic distribution of the eigenvalues of pseudodifferential operators in R n. Arkiv för Mathematik 17 (2) (1979) 297–313
S.M. KOZLOV, M.A. SUBIN: On the structure of functions of class S of self-adjoint elliptic operators on R n. Comm. of the Moscov Math. Soc. Russian Math. Surveys. 37 (2) 221–222 (1982)
A. MARTIN: Bound states in the Strong Coupling Limit. Helv. Phys. Acta 45 (1972) 140–148
A. MOHAMED: Etude spectrale des opérateurs pseudodifférentiels hypoelliptiques. Thèse de Doctorat. Univ. de Nantes 1983
D. ROBERT: Propriétés spectrales d'opérateurs pseudodifférentiels. Comm. in Partial Differential Equations 3 (9) (1978) 755–826
B. SIMON: On the number of bound states of two body Schrödinger operators. A review. Studies in Math. Physics. Princeton University Press 1976
V.N. TULOVSKII, M.A. SUBIN: On asymptotic distribution of eigenvalues of pseudodifferential operators in R n. Math. USSR Sbornik 21 (4) (1973) 565–583
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this chapter
Cite this chapter
Dauge, M., Robert, D. (1987). Weyl's formula for a class of pseudodifferential operators with negative order on L2(Rn). In: Cordes, H.O., Gramsch, B., Widom, H. (eds) Pseudo-Differential Operators. Lecture Notes in Mathematics, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077739
Download citation
DOI: https://doi.org/10.1007/BFb0077739
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17856-9
Online ISBN: 978-3-540-47886-7
eBook Packages: Springer Book Archive