Helffer, B.; Robert, D. Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles. (French) Zbl 0524.35103 J. Funct. Anal. 53, 246-268 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 99 Documents MSC: 35S05 Pseudodifferential operators as generalizations of partial differential operators 35A22 Transform methods (e.g., integral transforms) applied to PDEs 44A15 Special integral transforms (Legendre, Hilbert, etc.) 35B20 Perturbations in context of PDEs 35P05 General topics in linear spectral theory for PDEs Keywords:Mellin’s transform; functional calculus; semi-classical behaviour; discrete spectrum; Schrödinger operators; Dirac operators Citations:Zbl 0482.35069; Zbl 0246.35082 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Albeverio, S.; Blanchard, P.; Høegh-krohn, R., Feynman path integrals and the trace formula for the Schrödinger operators, Comm. Math. Phys., 83, 49-76 (1982) · Zbl 0493.35039 [2] Balian, R.; Bloch, C., Solution of the Schrödinger equation in terms of classical path, Ann. Phys., 85, 514-545 (1974) · Zbl 0281.35029 [3] Berry, M. V.; Mount, K. E., Semi-classical approximations in wave mechanics, Rep. Progr. Phys., 35, 315-397 (1972) [5] Chazarain, J., Spectre d’un hamiltonien quantique et mécanique classique, Comm. Partial Differential Equations, 5, 6, 595-644 (1980) · Zbl 0437.70014 [6] de Verdière, Y. Colin, Spectre conjoint d’opérateurs pseudodifférentiels qui commutent. I, Duke Math. J., 46, 169-182 (1979) · Zbl 0411.35073 [7] Combes, J. M.; Schrader, R.; Seiler, R., Classical bounds and limits of energy distributions of Hamiltonian operators in electromagnetic fields, Ann. Phys., 111, 1-18 (1978) [8] Grammaticos, B.; Voros, A., Semi-classical approximations of nuclear Hamiltonians. I. Spin independant potentials, Ann. Phys., 123, 359-380 (1979) [9] Helffer, B.; Robert, D., Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques, Ann. Inst. Fourier (Grenoble), 31, 3, 169-223 (1981) · Zbl 0451.35022 [10] Helffer, B.; Robert, D., Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques, Ann. École Mat. Sup. (Pise), IX, 3, 405-431 (1982) · Zbl 0507.35066 [11] Hörmander, L., The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math., 32, 359-443 (1979) · Zbl 0388.47032 [12] Kato, T., Pertubation Theory (1966), Springer-Verlag: Springer-Verlag New York · Zbl 0148.12601 [13] Maslov, V. P.; Feydoriuk, M. V., Semi classical Approximation in Quantum Mechanics, (MPAM No. 7 (1981), Reidel: Reidel Dordrecht) · Zbl 0458.58001 [14] Reed, M.; Simon, B., Analysis of operators, (Methods of Modern Mathematical Physics, Vol. IV (1978), Academic Press: Academic Press New York) · Zbl 0517.47006 [15] Robert, D., Calcul fonctionnel sur les opérateurs admissibles et application, J. Funct. Anal., 45, 74-94 (1982) · Zbl 0482.35069 [16] Robert, D., Propriétés spectrales d’opérateurs pseudodifférentiels, Comm. Partial Differential Equations, 3, 755-826 (1978) · Zbl 0392.35056 [17] Rondeaux, C., Classes de Schatten d’opérateurs pseudodifférentiels, Thèse de 3e cycle (1980), Reims · Zbl 0453.47028 [18] Seeley, R., Complex powers of an elliptic operator, (Proc. Symp. Pure Math., 10 (1967)), 288-307 · Zbl 0159.15504 [19] Strichartz, R. S., A functionnal calculus for elliptic pseudodifferential operators, Amer. J. Math., 94, 711-722 (1972) · Zbl 0246.35082 [21] Titchmarch, E. C., Introduction to the Theory of Fourier Integrals (1948), Oxford Univ. Press (Clarendon): Oxford Univ. Press (Clarendon) London/New York [22] Tulovskii, V. N.; Shubin, M. A., On the asymptotic distribution of eigenvalues of pseudodifferential operators in \(R^n\), Math. USSR-Sb., 21, 565-583 (1973) · Zbl 0295.35068 [23] Shubin, M. A., Opérateurs pseudodifférentiels et théorie spectrale (1978), Nauka, [Russe] · Zbl 0451.47064 [24] Voros, A., An algebra of pseudodifferential operators and the asymptotics of quantum mechinics, J. Funct. Anal., 29, 104-132 (1978) · Zbl 0386.47031 [25] Widom, H., Asymptotic expansions of determinants for families of trace class operators, Indiana Univ. Math. J., 27, 3, 449-479 (1978) · Zbl 0355.35076 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.