This is a preview of subscription content, log in via an institution to check access.
Literature cited
H. Weyl, “Quantenmechanik und Gruppentheorie,” Z. Phys.,46, 1–46 (1927).
R. Anderson, “The Weyl functional calculus,” J. Func. Anal.,4, No. 2, 240–267 (1969).
V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973).
V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], Moscow State Univ., Moscow (1965).
L. Hörmander, “Pseudodifferential operators,” in: Pseudodifferential Operators [Russian translation], Mir, Moscow (1967), pp. 63–87.
V. V. Kucherenko, “Commutation formula of a pseudodifferential operator with a rapidly oscillating exponential,” Mat. Sb.,94, 89–113 (1974).
Yu. L. Daletskii and S. G. Krein, “Integration and differentiation of operators depending on parameters,” Usp. Mat. Nauk,12, No. 1, 182–186 (1957).
F. A. Berezin, “Some remarks on the enveloping algebra of a Lie algebra,” Funkts. Anal. Prilozhen.,1, No. 2, 1–14 (1967).
R. Ya. Grabovskaya and S. G. Krein, “On a permutation formula for functions of operators representing a Lie algebra,” Funkts. Anal. Prilozhen.,7, No. 3, 81 (1973).
V. P. Maslov, “Use of operator methods for obtaining exact solutions,” Teor. Mat. Fiz.,33, No. 2, 185–209 (1977).
M. V. Karasev and V. P. Maslov, “Algebras with general commutation relations and their applications. II. Unitarily nonlinear operator equations,” in: Modern Problems in Mathematics [in Russian], Vol. 13, VINITI (1979), pp. 145–267.
M. V. Karasev, “On the theory of continuous integrals,” Usp. Mat. Nauk,31, No. 2, 213–214 (1976).
M. V. Karasev, “Expansion of functions of noncommuting operators,” Dokl. Akad. Nauk SSSR,214, No. 6, 1254–1257 (1974).
M. V. Karasev, “Some formulas for functions of ordered operators,” Mat. Zametki,18, No. 2, 267–277 (1975).
M. V. Karasev, “On ordered quantization,” Deposited at VINITI, Dep. No. 304-75, Moscow (1975).
M. V. Karasev, “The composition of a pseudodifferential operator and an operator with oscillating symbol, ”Deposited at VINITI, Dep. No. 303-75, Moscow (1975).
M. V. Karasev and V. E. Nazaikinskii, “On quantization of rapidly oscillating symbols,” Mat. Sb.,106, No. 2, 183–213 (1978).
M. V. Karasev, “Operators of the regular representation for class of nonlie commutation relations,” Funkts. Anal. Prilozhen.,13, No. 3, 91–92 (1979).
V. P. Maslov and V. E. Nazaikinskii, “Algebras with general commutation relations and their applications. I. Pseudodifferential equations with increasing coefficients,” in: Modern Problems in Mathematics [in Russian], Vol. 13, VINITI (1979), pp. 5–144.
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 26, No. 6, pp. 885–907, December, 1979.
Rights and permissions
About this article
Cite this article
Karasev, M.V. Weyl and ordered calculus of noncommuting operators. Mathematical Notes of the Academy of Sciences of the USSR 26, 945–958 (1979). https://doi.org/10.1007/BF01142081
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01142081