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A note on inductive limit model of Bargmann space of infinite order

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Języki publikacji
EN
Abstrakty
EN
It is shown that the generalized creation and annihilation operators on Bargmann space of infinite order in a direction a = (a1, a2, ...) mem l2 are inductive limits of the creation and annihilation operator acting on Bargmann space on n-th order.
Rocznik
Strony
139--148
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland, stochel@uci.agh.edu.pl
Bibliografia
  • [1] Bargmann V.: On a Hilbert space of analytic functions and associated integral transform I. Comm. Pure Appl. Math. 14 (1961), 187-214.
  • [2] Bargman V.: Remarks on a Hilbert space of analityc functions. Proc. Nat.Acad. Sci. U.S.A. 48 (1962), 199-204.
  • [3] Berger C. A., Coburn L. A.: Toeplitz operators and quantum mechanics. J. Funct. Anal. 68 (1986), 273-299.
  • [4] Berger C.A., Coburn L.A.: Toeplitz operators on the Segal-Bargmann space. Trans. Amer. Math. Soc. 301 (1987), 813-829.
  • [5] Bergman S.: The kernel function and conformal mapping. Math. Surveys 5 (1950), Amer. Math. Soc. Providance. R.I.
  • [6] Cook J.M.: The mathematics of second quantization. Trans. Amer. Math. Soc. 74 (1953), 222-245.
  • [7] Dinnen S.: Complex analysis in locally convex spaces. North Holand, Math. Stud. 57 (1981).
  • [8] Friedrichs K.O.: Mathematical aspect of the quantum theory of fields. New York, lnterscience, 1953.
  • [9] Guichardet A.: Symmetric Hilbert spaces and related topics. Lecture Notes in Math. 261 (1972), Springer-Verlag.
  • [10] Janas J.: Inductive limit of operators and its applications. Studia Math. 90 (1988), 87-102.
  • [11] Janas J.: Unbounded Toeplitz operators in the Bargmann-Segal space. Studia Math. 99 (1991), 87-99.
  • [12] Janas J.: Unbounded Toeplitz operators in the Bargmann-Segal space III. Studia Math. 112 (1994), 75-82.
  • [13] Janas J., Rudol K.: Toeplitz operators on the Barg mann-Segal space of infinitely many variables. Operator Theory: Adv. Appl. 43 (1990), 87-102.
  • [14] Janas J., Rudol K.: Toeplitz Operators in infinitely many variables. In: Topics in Operator Theory, Operator Algebras and Applications, XV-th Internat. Conf. in Operator Theory, Timisoara 1994. A. Gheondea et al. (Eds) IMAR, Bucharest 1995, 147-160.
  • [15] Janas J., Stochel J.: Unbounded Toeplitz operators on the Segal-Bargmann space II. J. Funct.Anal. 126 (1994), 418-447.
  • [16] Kuo H. H.: Gaussian measures in Banach spaces. Lec. Notes in Math. 463, Springer-Verlag 1975.
  • [17] Szafraniec F.H.: An inductive limit procedure within the quantum harmonic osci-lator. Operator Theory Adv. Appl. vol. 106 (1988), 389-395.
  • [18] Segal I.E.: Lectures at the Summer Seminar on Applied Math. Boulder Colorado 1960.
  • [19] Segal I.E.: The complex wave representation of the free boson field. Adv. in Math., Supp. Studies 3 (1978), 321-343.
  • [20] Stochel J.B.: A remark on Bargmann's Hilbert space of an infinite order. Opu-scula Math. 10 (1991), 171-181.
  • [21] Stochel J. B.: Subnormality of generalized creation operators on Bargmann's space of an infinite order. Integr. Equat. Oper. Th. 15 (1992), 1011-1032.
  • [22] Stochel J.B.: A remark on Bargmann's space of an infinite order II. Opuscula Math. 16 (1996), 97-110.
  • [23] Stochel J.B.: Remark on representation of generalized creation and annihilation operators in a Fock space. Universitatis Iagellonicae Acta Math. 34 (1997), 135-148.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0001-0024
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