Spectral mapping theorem for fractional powers in locally convex spaces

Celso Martínez; Miguel Sanz

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 24, Issue: 4, page 685-702
  • ISSN: 0391-173X

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Martínez, Celso, and Sanz, Miguel. "Spectral mapping theorem for fractional powers in locally convex spaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24.4 (1997): 685-702. <http://eudml.org/doc/84274>.

@article{Martínez1997,
author = {Martínez, Celso, Sanz, Miguel},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {fractional powers of nonnegative operators; sequentially complete, locally convex spaces; spectral mapping theorem; functional calculus},
language = {eng},
number = {4},
pages = {685-702},
publisher = {Scuola normale superiore},
title = {Spectral mapping theorem for fractional powers in locally convex spaces},
url = {http://eudml.org/doc/84274},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Martínez, Celso
AU - Sanz, Miguel
TI - Spectral mapping theorem for fractional powers in locally convex spaces
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 24
IS - 4
SP - 685
EP - 702
LA - eng
KW - fractional powers of nonnegative operators; sequentially complete, locally convex spaces; spectral mapping theorem; functional calculus
UR - http://eudml.org/doc/84274
ER -

References

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  1. [1] A.V. Balakrishnan, Fractional powers of closed operators and semigroups generated by them, Pacific J. Math.10 (1960), 419-437. Zbl0103.33502MR115096
  2. [2] N. Dunford - J.T. Schwartz, Linear Operators. Part I: General Theory, Interscience Publishers, John Wiley & Sons, 1958. Zbl0084.10402MR1009162
  3. [3] F. Hirsch, Intégrales de résolvantes et calcul symbolique, Ann. Inst. Fourier, Grenoble22 (1972), 239-264. Zbl0235.47007MR367716
  4. [4] F. Hirsch, Domaines d'opérateurs représentés comme integrales de résolvantes, J. Funct. Anal.23 (1976), 199-217. Zbl0341.47013MR428105
  5. [5] H. Komatsu, Fractional powers of operators, II. Interpolation spaces, Pacific J. Math.21 (1967),89-111. Zbl0168.10702MR206716
  6. [6] W. Lamb, Fractional powers of operators defined on a Frechet space, Proc. Edinburgh Math. Soc. 27 (1984), 165-181. Zbl0527.47002MR760612
  7. [7] W. Lamb - A.C. Mcbride, On relating two approaches to fractional calculus, J. Math. Anal. Appl.132 (1988), 590-610. Zbl0651.26007MR943531
  8. [8] C. Martínez - M. Sanz, Fractional powers of non-densely defined operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1991), 443-454. Zbl0811.47013MR1145317
  9. [9] C. Martínez - M. Sanz - V. Calvo, Fractional powers of non-negative operators in Fréchet spaces, Internat. J. Math. Math. Sci.12 (1989), 309-320. Zbl0684.47013MR994914
  10. [10] C. Martínez - M. Sanz - L. Marco, Fractional powers of operators, J. Math. Soc. Japan40 (1988), 331-347. Zbl0628.47006MR930604
  11. [11] C. Martínez - M. Sanz - M.D. Martínez, Some inequalities for fractional integrals and derivatives, Dokl. Akad. Nauk SSSR315 (1990), 1049-1051 (Russian). English translation in Soviet Math. Dokl. 42 (1991), 876-879. Zbl0754.47026MR1100377
  12. [12] C. Martínez - M. Sanz - M.D. Martínez, About Fractional Integrals in the Space of Locally Integrable Functions, J. Math. Anal. Appl.167 (1992), 111-122. Zbl0760.47016MR1165261
  13. [13] S.E. Schiavone - W. Lamb, A fractional power approach to fractional calculus, J. Math. Anal. Appl.149 (1990), 111-122. Zbl0707.47012MR1057681
  14. [14] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N. J., 1970. Zbl0207.13501MR290095

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