Skip to main content
SpringerLink
Log in

Hyperfunction semigroups

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We analyze Fourier hyperfunction and hyperfunction semigroups with nondensely defined generators and their connections with local convoluted C-semigroups. Structural theorems and spectral characterizations give necessary and sufficient conditions for the existence of these semigroups generated by a closed possibly not densely defined operator A.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kostić M. and Pilipović S., “Ultradistribution semigroups,” Siberian Math. J., 53, No. 2, 232–242 (2012).

    Article  MATH  Google Scholar 

  2. Kostić M., Pilipović S., and Velinov D., “Structural theorems for¿ltradistribution semigroups,” Siberian Math. J., 56, No. 1, 83–91 (2015).

    Article  Google Scholar 

  3. Lions J. L., “Les semi-groupes distributions,” Portugal. Math., 19, No. 3–4, 141–164 (1960).

    MathSciNet  MATH  Google Scholar 

  4. Chazarain J., “Problémes de Cauchy abstraites et applications ´a quelques problémes mixtes,” J. Funct. Anal., 7, 386–446 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  5. Ito Y., “On the abstract Cauchy problems in the sense of Fourier hyperfunctions,” J. Math. Tokushima¿niv., 16, 25–31 (1982).

    MATH  Google Scholar 

  6. Kisyński J., “Distribution semigroups and one parameter semigroups,” Bull. Polish Acad. Sci., 50, 189–216 (2002).

    MATH  Google Scholar 

  7. Kostić M., “C-Distribution semigroups,” Studia Math., 185, 201–217 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  8. Kunstmann P. C., “Distribution semigroups and abstract Cauchy problems,” Trans. Amer. Math. Soc., 351, 837–856 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  9. Ouchi S., “Hyperfunction solutions of the abstract Cauchy problems,” Proc. Japan Acad., 47, 541–544 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  10. Ouchi S., “On abstract Cauchy problems in the sense of hyperfunctions in hyperfunctions and pseudo-differential equations,” in: Proc. Katata, 1971 (ed. H. Komatsu), Springer-Verlag, Berlin, 1973, pp. 135–152 (Lect. Notes Math.; V. 287).

    Google Scholar 

  11. Kochubei A. N., “Hyperfunction solutions of differential-operator equations,” Siberian Math. J., 20, No. 4, 778–791 (1979).

    MathSciNet  Google Scholar 

  12. Beals R., “On the abstract Cauchy problem,” J. Funct. Anal., 10, 281–299 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  13. Ito Y., “Fourier hyperfunction semigroups,” J. Math. Tokushima¿niv., 16, 33–53 (1982).

    MATH  Google Scholar 

  14. Kaneko A., Introduction to Hyperfunctions, Kluwer Academic Publishers, Dordrecht, Boston, and London (1982).

    Google Scholar 

  15. Morimoto M., An Introduction to Sato’s Hyperfunctions, Amer. Math. Soc., Providence (1993) (Transl. Math. Monogr.; V. 129).

    Google Scholar 

  16. Hörmander L., “Between distributions and hyperfunctions,” in: Astérisque, Vol. 131 (Colloq. Honneur L. Schwartz, Ec. Polytech., 1983), 1985, pp. 89–106.

    Google Scholar 

  17. Kawai T., “The theory of Fourier transformations in the theory of hyperfunctions and its applications,” Surikaisekikenkyusho Kokyuroku, 108, 84–288 (1969).

    Google Scholar 

  18. Kawai T., “On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients,” J. Fac. Sci.¿niv. Tokyo Sect. IA Math., 17, 465–517 (1970).

    Google Scholar 

  19. Komatsu H., An Introduction to the Theory of Generalized Functions, Iwanami Shoten, Tokyo (1978).

    Google Scholar 

  20. Sato M., “Theory of hyperfunctions,” S¿gaku, 10, 1–27 (1958).

    MATH  Google Scholar 

  21. Chung J., Chung S.-Y., and Kim D., “Characterization of the Gelfand–Shilov spaces via Fourier transforms,” Proc. Amer. Math. Soc., 124, 2101–2108 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  22. Chung J., Chung S.-Y., and Kim D., “A characterization for Fourier hyperfunctions,” Publ. Res. Inst. Math. Sci., 30, 203–208 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  23. Komatsu H., “Ultradistributions. I: Structure theorems and a characterization,” J. Fac. Sci.¿niv. Tokyo Sect. IA Math., 20, No. 1, 25–105 (1973).

    MathSciNet  MATH  Google Scholar 

  24. Komatsu H., “Ultradistributions. III: Vector valued¿ltradistributions and the theory of kernels,” J. Fac. Sci.¿niv. Tokyo Sect. IA Math., 29, 653–718 (1982).

    MathSciNet  MATH  Google Scholar 

  25. Komatsu H., “Operational calculus and semi-groups of operators,” in: Functional Analysis and Related Topics, Berlin, 1991, pp. 213–234.

    Google Scholar 

  26. Kunstmann P. C., “Stationary dense operators and generation of non-dense distribution semigroups,” J. Operator Theory, 37, No. 1, 111–120 (1997).

    MathSciNet  MATH  Google Scholar 

  27. Arendt W., El-Mennaoui O., and Keyantuo V., “Local integrated semigroups: evolution with jumps of regularity,” J. Math. Anal. Appl., 186, 572–595 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  28. Hieber M., “Integrated semigroups and differential operators on Lp spaces,” Math. Ann., 29, 1–16 (1991).

    Article  MathSciNet  Google Scholar 

  29. Melnikova I. V. and Filinkov A. I., Abstract Cauchy Problems: Three Approaches, Chapman and Hall/CRC,Washington (2001).

    Book  Google Scholar 

  30. Arendt W., Batty C. J. K., Hieber M., and Neubrander F., Vector-Valued Laplace Transforms and Cauchy Problems, Birkhäuser-Verlag, Basel (2001).

    Book  MATH  Google Scholar 

  31. Kostić M. and Pilipović S., “Global convoluted semigroups,” Math. Nachr., 280, No. 15, 1727–1743 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  32. Ciorănescu I. and Lumer G., “Problèmes d’évolution régularisés par¿n noyan général K(t). Formule de Duhamel, prolongements, théorèmes de génération,” C. R. Acad. Sci. Paris Sér. I. Math., 319, No. 12, 1273–1278 (1995).

    Google Scholar 

  33. Kostić M., Generalized Semigroups and Cosine Functions, Math. Inst., Belgrade (2011).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    M. Kostić

  2. University of Novi Sad, Novi Sad, Serbia

    S. Pilipović

  3. Department for Mathematics, Faculty of Civil Engineering, University Ss. Cyril and Methodius–Skopje, Skopje, Macedonia

    D. Velinov

Authors
  1. M. Kostić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Pilipović
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Velinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Kostić.

Additional information

Original Russian Text Copyright © 2015 Kostić M., Pilipović S., and Velinov D.

Novi Sad; Skopje. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 4, pp. 821–834, July–August, 2015; DOI: 10.17377/smzh.2015.56.409.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kostić, M., Pilipović, S. & Velinov, D. Hyperfunction semigroups. Sib Math J 56, 650–661 (2015). https://doi.org/10.1134/S0037446615040096

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446615040096

Keywords

Search

Navigation