The Taylor transformation of analytic functionals with non-bounded carrier

Grzegorz Łysik

Studia Mathematica (1994)

  • Volume: 108, Issue: 2, page 159-176
  • ISSN: 0039-3223

Abstract

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Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.

How to cite

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Łysik, Grzegorz. "The Taylor transformation of analytic functionals with non-bounded carrier." Studia Mathematica 108.2 (1994): 159-176. <http://eudml.org/doc/216047>.

@article{Łysik1994,
abstract = {Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.},
author = {Łysik, Grzegorz},
journal = {Studia Mathematica},
keywords = {image of the space of analytic functionals with non-bounded carrier; multipliers; Taylor transformation; representation of analytic functionals; boundary value of holomorphic functions},
language = {eng},
number = {2},
pages = {159-176},
title = {The Taylor transformation of analytic functionals with non-bounded carrier},
url = {http://eudml.org/doc/216047},
volume = {108},
year = {1994},
}

TY - JOUR
AU - Łysik, Grzegorz
TI - The Taylor transformation of analytic functionals with non-bounded carrier
JO - Studia Mathematica
PY - 1994
VL - 108
IS - 2
SP - 159
EP - 176
AB - Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.
LA - eng
KW - image of the space of analytic functionals with non-bounded carrier; multipliers; Taylor transformation; representation of analytic functionals; boundary value of holomorphic functions
UR - http://eudml.org/doc/216047
ER -

References

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  1. [1] E. Hille, Analytic Function Theory, Vols. 1 and 2, Chelsea, New York, 1959, 1962. Zbl0088.05204
  2. [2] G. Łysik, Generalized Taylor expansions of singular functions, Studia Math. 99 (1991), 235-262. Zbl0742.46022
  3. [3] M. Morimoto, Analytic functionals with non-compact carrier, Tokyo J. Math. 1 (1978), 77-103. Zbl0384.46027
  4. [4] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Kluwer, Dordrecht, 1992. Zbl0771.35002
  5. [5] J. C. Tougeron, Gevrey expansions and applications, preprint, University of Toronto, 1991. 
  6. [6] B. Ziemian, The Mellin transformation and multidimensional generalized Taylor expansions of singular functions, J. Fac. Sci. Univ. Tokyo 36 (1989), 263-295. Zbl0713.46025
  7. [7] B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics I, J. Differential Equations 101 (1993), 28-57. Zbl0777.47028
  8. [8] B. Ziemian, Generalized Analytic Functions, book in preparation. 

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