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TMF, 1979, Volume 39, Number 3, Pages 291–301 (Mi tmf2842)  

This article is cited in 12 scientific papers (total in 12 papers)

Algebra of one-dimensional generalized functions

Yu. M. Shirokov


Abstract: An associative algebra $\mathscr{A}$, equipped with involution and differentiation, is constructed for generalized functions of one variable that at one fixed point can have singularities like the delta function and its derivatives and also finite discontinuities for the function and all its derivatives. The elements of $\mathscr{A}$ together with the differentiation operator form the algebra of local observables for a quantum theory with indefinite metric and state vectors that are also generalized functions. By going over to a smaller space, one can obtain quantum models with positive metric and with strongly singular concentrated potentials.

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English version:
Theoretical and Mathematical Physics, 1979, 39:3, 471–477

Bibliographic databases:

Received: 21.12.1978

Citation: Yu. M. Shirokov, “Algebra of one-dimensional generalized functions”, TMF, 39:3 (1979), 291–301; Theoret. and Math. Phys., 39:3 (1979), 471–477

Citation in format AMSBIB
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\by Yu.~M.~Shirokov
\paper Algebra of one-dimensional generalized functions
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\yr 1979
\vol 39
\issue 3
\pages 291--301
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\transl
\jour Theoret. and Math. Phys.
\yr 1979
\vol 39
\issue 3
\pages 471--477
\crossref{https://doi.org/10.1007/BF01017992}
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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. Yu. M. Shirokov, “Algebra of three-dimensional generalized functions”, Theoret. and Math. Phys., 40:3 (1979), 790–794  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. M. Shirokov, “Strongly singular potentials in one-dimensional quantum mechanics”, Theoret. and Math. Phys., 41:2 (1979), 1031–1038  mathnet  crossref  mathscinet  zmath  isi
    3. Yu. M. Shirokov, “Strongly singular potentials in three-dimensional quantum mechanics”, Theoret. and Math. Phys., 42:1 (1980), 28–31  mathnet  crossref  mathscinet  isi
    4. Yu. M. Shirokov, “Representation of free solutions for Schrödinger equations with strongly singular concentrated potentials”, Theoret. and Math. Phys., 46:3 (1981), 191–196  mathnet  crossref  mathscinet  zmath  isi
    5. G. K. Tolokonnikov, Yu. M. Shirokov, “Associative algebra of generalized functions closed with respect to differentiation and integration”, Theoret. and Math. Phys., 46:3 (1981), 200–203  mathnet  crossref  mathscinet  zmath  isi
    6. S. V. Talalov, Yu. M. Shirokov, “Interaction of a charged particle with an external electromagnetic field in the presence of a strongly singular potential”, Theoret. and Math. Phys., 46:3 (1981), 207–210  mathnet  crossref  mathscinet  isi
    7. O. G. Goryaga, Yu. M. Shirokov, “Energy levels of an oscillator with singular concentrated potential”, Theoret. and Math. Phys., 46:3 (1981), 210–212  mathnet  crossref  mathscinet  zmath  isi
    8. G. K. Tolokonnikov, “Shirokov algebras. I”, Theoret. and Math. Phys., 51:3 (1982), 554–561  mathnet  crossref  mathscinet  zmath  isi  elib
    9. V. A. Smirnov, “Associative algebra of functionals containing $\delta(x)$ and $r^n$”, Theoret. and Math. Phys., 52:2 (1982), 832–835  mathnet  crossref  mathscinet  zmath  isi
    10. G. K. Tolokonnikov, “Differential rings used in Shirokov algebras”, Theoret. and Math. Phys., 53:1 (1982), 952–954  mathnet  crossref  mathscinet  zmath  isi
    11. V. M. Shelkovich, “Associative and commutative distribution algebra with multipliers, and generalized solutions of nonlinear equations”, Math. Notes, 57:5 (1995), 536–549  mathnet  crossref  mathscinet  zmath  isi  elib
    12. V. G. Danilov, V. P. Maslov, V. M. Shelkovich, “Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems”, Theoret. and Math. Phys., 114:1 (1998), 1–42  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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