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Differential Equations

, Volume 46, Issue 2, pp 224–238 | Cite as

On some classes of infinitely differentiable operator semigroups

  • M. S. Bichegkuev
Partial Differential Equations

Abstract

Given a linear relation (a multivalued linear operator), we construct an infinitely differentiable operator semigroup and study its properties.

Keywords

Banach Space Cauchy Problem Linear Relation Banach Algebra Basic Generator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Hille, E. and Phillips, R., Functional Analysis and Semi-Groups, Providence, 1957. Translated under the title Funktsional’nyi analiz i polugruppy, Moscow: Inostrannaya literatura, 1963.Google Scholar
  2. 2.
    Baskakov, A.G., Linear Relations as Generators of Operator Semigroups, Mat. Zametki, 2008, vol. 84, no. 2, pp. 175–192.MathSciNetGoogle Scholar
  3. 3.
    Sil’chenko, Yu.T., On a Class of Semigroups, Funktsional Anal. i Prilozhen., 1999, vol. 33, no. 4, pp. 90–93.MathSciNetGoogle Scholar
  4. 4.
    Sil’chenko, Yu.T., Semigroups with Nondensely Defined Generating Operator, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 7, pp. 57–62.Google Scholar
  5. 5.
    Sobolevskii, P.E., Semigroups of Growth α, Dokl. Akad. Nauk SSSR, 1971, vol. 196, no. 3, pp. 535–537.MathSciNetGoogle Scholar
  6. 6.
    Krein, S.G., Lineinye differentsial’nye uravneniya v banakhovom prostranstve (Linear Differential Equations in a Banach Space), Moscow: Nauka, 1967.Google Scholar
  7. 7.
    Bichegkuev, M.S., On a Weakened Cauchy Problem for a Linear Differential Inclusion, Mat. Zametki, 2006, vol. 79, no. 4, pp. 483–487.MathSciNetGoogle Scholar
  8. 8.
    Da Prato, G., Semigruppi di crescenza n, Ann. Sc. Norm. Super. Pisa Sci. Fis. Mat., 1966, vol. 20, no. 3, pp. 753–782.zbMATHGoogle Scholar
  9. 9.
    Zabreiko, P.P. and Zafievskii, A.V., A Certain Class of Semigroups, Dokl. Akad. Nauk SSSR, 1969, vol. 189, pp. 934–937.MathSciNetGoogle Scholar
  10. 10.
    Zafievskii, A.V., Semigroups That Have Singularities Summable with a Power Weight at Zero, Dokl. Akad. Nauk SSSR, 1970, vol. 195, pp. 24–27.MathSciNetGoogle Scholar
  11. 11.
    Zafievskii, A.V., New Classes of Semigroups, Vestn. Yaroslav. Univ., 1974, vol. 8, pp. 53–77.MathSciNetGoogle Scholar
  12. 12.
    Baskakov, A.G. and Chernyshov, K.I., Spectral Analysis of Linear Relations, and Degenerate Semigroups of Operators, Mat. Sb., 2002, vol. 193, no. 11, pp. 3–42.MathSciNetGoogle Scholar
  13. 13.
    Cross, R., Multivalued Linear Operators, New York, 1998.Google Scholar
  14. 14.
    Favini, A. and Yagi, A., Degenerate Differential Equations in Banach Spaces, New York, 1998.Google Scholar
  15. 15.
    Fedorov, V.I., Relaxed Solutions of a Sobolev-Type Linear Equation and Semigroups of Operators, Izv. Ross. Akad. Nauk Ser. Mat., 2003, vol. 67, no. 4, pp. 171–188.MathSciNetGoogle Scholar
  16. 16.
    Sobolev, S.L., Cauchy’s Problem for a Partial Case of Systems Not Belonging to the Kowalewsky Type, Dokl. Akad. Nauk SSSR, 1952, vol. 82, no. 2, pp. 205–208.zbMATHMathSciNetGoogle Scholar
  17. 17.
    Gal’pern, S.A., Cauchy Problem for General Systems of Linear Partial Differential Equations, Dokl. Akad. Nauk SSSR, 1958, vol. 119, no. 4, pp. 640–643.zbMATHMathSciNetGoogle Scholar
  18. 18.
    Sil’chenko, Yu.T., Eigenvalues and Eigenfunctions of a Differential Operator with Nonlocal Boundary Conditions, Differ. Uravn., 2006, vol. 42, no. 6, pp. 764–768.MathSciNetGoogle Scholar
  19. 19.
    Thomas, J., Untersuchungen über das Eigenwertproblem d/dx(f(x)dy/dx) + λg(x)y = 0, ∫ab A(x)y(x)dx = ∫ab B(x)y(x)dx = 0, Math. Nachr., 1951, no. 6, pp. 229–261.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • M. S. Bichegkuev
    • 1
  1. 1.Khetagurov North Ossetian State UniversityVladikavkazRussia

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