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2000 | 53 | 1 | 79-88
Tytuł artykułu

The Weyl correspondence as a functional calculus

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to use an abstract realization of the Weyl correspondence to define functions of pseudo-differential operators. We consider operators that form a self-adjoint Banach algebra. We construct on this algebra a functional calculus with respect to functions which are defined on the Euclidean space and have a finite number of derivatives.
Słowa kluczowe
Rocznik
Tom
53
Numer
1
Strony
79-88
Opis fizyczny
Daty
wydano
2000
Twórcy
  • Department of Mathematics, New Mexico State University, Las Cruces, NM 88003-8001, U.S.A.
Bibliografia
  • [1] J. Alvarez, Existence of a functional calculus on certain algebras of pseudo-differential operators, J. Unión Mat. Argentina 29 (1979), 55-76.
  • [2] J. Alvarez and A. P. Calderón, Functional calculi for pseudo-differential operators, I, in: Proceedings of the Seminar on Fourier Analysis held at El Escorial, June 17-23, 1979,edited by Miguel de Guzmán and Ireneo Peral, Asociación Matemática Española 1, 1979, 1-61.
  • [3] J. Alvarez, An algebra of $L^p$-bounded pseudo-differential operators, J. Math. Anal. Appl. 84 (1983) 268-282.
  • [4] J. Alvarez and A. P. Calderón, Functional calculi for pseudo-differential operators, II, in: Studies in Applied Mathematics, edited by Victor Guillemin, Academic Press, New York, 1983, 27-72.
  • [5] J. Alvarez, Functional calculi for pseudo-differential operators, III, Studia Mathematica 95 (1989), 53-71.
  • [6] J. Alvarez and J. Hounie, Functions of pseudo-differential operators of non-positive order, J. Funct. Anal. 141 (1996), 45-59.
  • [7] R. F. V. Anderson, The Weyl functional calculus, J. Funct. Anal. 4 (1969), 240-267.
  • [8] A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901-921.
  • [9] R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York and London, 1972.
  • [10] G. B. Folland, Harmonic analysis in phase space, Princeton University Press, Princeton, New Jersey, 1989.
  • [11] L. Hörmander, The Weyl calculus of pseudo-differential operators, Comm. Pure and Appl. Math. 32 (1965), 269-305.
  • [12] L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symp. Pure Math. 10, Amer. Math. Soc., 1966, 138-183.
  • [13] J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure and Appl. Math. 18 (1979), 359-443.
  • [14] M. L. Lapidus, Quantification, calcul opérationnel de Feynman axiomatique et intégrale fonctionnelle généralisée, C. R. Acad. Sci. Paris Sér. I 308 (1989), 133-138.
  • [15] A. Mc Intosh and A. Pryde, A functional calculus for several commuting operators, Indiana Univ. Math. J. 36 (1987), 420-439.
  • [16] V. Nazaikinskii, V. Shatalov and B. Sternin, Methods of non-commutative analysis, de Gruyter Stud. Math. 22, de Gruyter, Berlin, 1996.
  • [17] E. Nelson, Operator differential equations, Lecture Notes, Princeton University (1964-1965).
  • [18] E. Nelson, Operants: A functional calculus for non-commuting operators, in: Functional analysis and related topics, edited by Felix E. Browder, Springer-Verlag, New York, 1970, 172-187.
  • [19] J. C. T. Pool, Mathematical aspects of the Weyl correspondence, J. Math. Physics 7 (1966) 66-76.
  • [20] M. Riesz and B. Szőkefalvi-Nagy, Functional analysis, Ungar, New York, 1955.
  • [21] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127-148.
  • [22] M. E. Taylor, Functions of several self-adjoint operators, Proc. Amer. Math. Soc. 19 (1968), 91-98.
  • [23] H. Weyl, Gruppentheorie und Quantenmechanik, Hirzel, Leipzig, 1928.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-bcpv53z1p79bwm
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