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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 6, Pages 1265–1291 (Mi izv1340)  

This article is cited in 14 scientific papers (total in 14 papers)

Infinite-dimensional pseudodifferential operators

A. Yu. Khrennikov


Abstract: A general theory is constructed for pseudodifferential operators on infinite-dimensional spaces. This theory is a natural basis for second quantization of field systems, as well as for quantization and second quantization of strings. Generalizations are considered to the case of infinite-dimensional superspaces (quantization and second quantization of superstrings, fermion fields, gauge theory of boson and fermion strings).
Bibliography: 55 titles.

Full text: PDF file (3600 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 575–601

Bibliographic databases:

UDC: 517.948+513.8+519.4
MSC: Primary 35S05, 81E05, 26E15; Secondary 81C30, 35S10, 28C20, 47G05, 58D20, 58D30, 46N05, 6
Received: 17.10.1985

Citation: A. Yu. Khrennikov, “Infinite-dimensional pseudodifferential operators”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1265–1291; Math. USSR-Izv., 31:3 (1988), 575–601

Citation in format AMSBIB
\Bibitem{Khr87}
\by A.~Yu.~Khrennikov
\paper Infinite-dimensional pseudodifferential operators
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 6
\pages 1265--1291
\mathnet{http://mi.mathnet.ru/izv1340}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=933964}
\zmath{https://zbmath.org/?q=an:0685.35107|0658.35099}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 3
\pages 575--601
\crossref{https://doi.org/10.1070/IM1988v031n03ABEH001090}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Khrennikov, “Functional superanalysis”, Russian Math. Surveys, 43:2 (1988), 103–137  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Khrennikov, “The correspondence principle in quantum field theory and relativistic boson string theory”, Math. USSR-Sb., 67:1 (1990), 209–233  mathnet  crossref  mathscinet  isi
    3. A. Yu. Khrennikov, “Quantization of bosonic string field and infinite-dimensional pseudodifferential operators. Fixed gauge”, Theoret. and Math. Phys., 80:2 (1989), 829–838  mathnet  crossref  mathscinet  isi
    4. A. Yu. Khrennikov, “The Central Limit Theorem for a Quasi-Gaussian Distribution on an Infinite-Dimensional Superspace”, Theory Probab Appl, 35:3 (1990), 580  mathnet  crossref  mathscinet  zmath  isi
    5. A. Yu. Khrennikov, “Equatios on a superspace”, Math. USSR-Izv., 36:3 (1991), 597–627  mathnet  crossref  mathscinet  zmath  adsnasa
    6. A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. Yu. Khrennikov, “Quantum mechanics over non-Archimedean number fields”, Theoret. and Math. Phys., 83:3 (1990), 623–632  mathnet  crossref  mathscinet  zmath  isi
    8. A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Math. USSR-Izv., 39:1 (1992), 761–794  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. Yu. Daletskii, “Infinite-dimensional Schrödinger equations and the representation of a group of symplectomorphisms of a Hilbert phase space”, Funct. Anal. Appl., 26:1 (1992), 74–75  mathnet  crossref  mathscinet  zmath  isi
    10. A. Yu. Khrennikov, “The infinite-dimensional Liouville equation”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 17–41  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. Sergio Albeverio, Alexei Daletskii, “Asymptotic quantization for solution manifolds of some infinite dimensional Hamiltonian systems”, Journal of Geometry and Physics, 19:1 (1996), 31  crossref
    12. Sergio Albeverio, Alexei Daletskh, “Algebras of Pseudodifferential Operators inL2 Given by Smooth Measures on Hilbert Spaces”, Math Nachr, 192:1 (1998), 5  crossref  mathscinet  zmath  isi
    13. A. Yu. Khrennikov, H. Petersson, “A Paley–Wiener theorem for generalized entire functions on infinite-dimensional spaces”, Izv. Math., 65:2 (2001), 403–424  mathnet  crossref  crossref  mathscinet  zmath  elib
    14. A. Yu. Khrennikov, “Symplectic geometry on an infinite-dimensional phase space and an asymptotic representation of quantum averages by Gaussian functional integrals”, Izv. Math., 72:1 (2008), 127–148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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