On the ℒ -characteristic of fractional powers of linear operators

Jürgen Appell; Marilda A. Simões; Petr P. Zabrejko

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 1, page 21-34
  • ISSN: 0010-2628

Abstract

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We describe the geometric structure of the ℒ -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.

How to cite

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Appell, Jürgen, Simões, Marilda A., and Zabrejko, Petr P.. "On the $\mathcal {L}$-characteristic of fractional powers of linear operators." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 21-34. <http://eudml.org/doc/247631>.

@article{Appell1994,
abstract = {We describe the geometric structure of the $\{\mathcal \{L\}\}$-characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.},
author = {Appell, Jürgen, Simões, Marilda A., Zabrejko, Petr P.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {fractional powers of operators; $L$-characteristic; Lebesgue spaces; interpolation theorems; positive, self-adjoint, densely defined operator; interpolation theorem},
language = {eng},
number = {1},
pages = {21-34},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the $\mathcal \{L\}$-characteristic of fractional powers of linear operators},
url = {http://eudml.org/doc/247631},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Appell, Jürgen
AU - Simões, Marilda A.
AU - Zabrejko, Petr P.
TI - On the $\mathcal {L}$-characteristic of fractional powers of linear operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 21
EP - 34
AB - We describe the geometric structure of the ${\mathcal {L}}$-characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.
LA - eng
KW - fractional powers of operators; $L$-characteristic; Lebesgue spaces; interpolation theorems; positive, self-adjoint, densely defined operator; interpolation theorem
UR - http://eudml.org/doc/247631
ER -

References

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