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Criteria for Bochner's extension problem

Michael Ruzhansky (UGent) and Mitsuru Sugimoto
(2010) ASYMPTOTIC ANALYSIS. 66(3-4). p.125-138
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Abstract
A necessary and sufficient condition for the resolution of the weak extension problem is given. This criterion is applied to also give a criterion for the solvability of the classical Bochner's extension problem in the L(p)-category. The solution of the L(p)-extension problem by Bochner [J. Math. Pures Appl. 35 (1956), 193-202] giving the relation between the order of the operator, the dimension, and index p, for which the L(p)-extension property holds, can be viewed as a subcritical case of the general L(p)-extension problem. In general, this property fails in some critical and in all supercritical cases. In this paper, the L(p)-extension problem is investigated for operators of all orders and for all 1 <= p <= infinity. Necessary and sufficient conditions on the subset of L(p) are given for which the L(p)-extension property still holds, in the critical and supercritical cases.
Keywords
extension problem, removable singularities, PARTIAL-DIFFERENTIAL-EQUATIONS, REMOVABLE SINGULARITIES, THEOREM

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MLA
Ruzhansky, Michael, and Mitsuru Sugimoto. “Criteria for Bochner’s Extension Problem.” ASYMPTOTIC ANALYSIS, vol. 66, no. 3–4, 2010, pp. 125–38, doi:10.3233/ASY-2009-0962.
APA
Ruzhansky, M., & Sugimoto, M. (2010). Criteria for Bochner’s extension problem. ASYMPTOTIC ANALYSIS, 66(3–4), 125–138. https://doi.org/10.3233/ASY-2009-0962
Chicago author-date
Ruzhansky, Michael, and Mitsuru Sugimoto. 2010. “Criteria for Bochner’s Extension Problem.” ASYMPTOTIC ANALYSIS 66 (3–4): 125–38. https://doi.org/10.3233/ASY-2009-0962.
Chicago author-date (all authors)
Ruzhansky, Michael, and Mitsuru Sugimoto. 2010. “Criteria for Bochner’s Extension Problem.” ASYMPTOTIC ANALYSIS 66 (3–4): 125–138. doi:10.3233/ASY-2009-0962.
Vancouver
1.
Ruzhansky M, Sugimoto M. Criteria for Bochner’s extension problem. ASYMPTOTIC ANALYSIS. 2010;66(3–4):125–38.
IEEE
[1]
M. Ruzhansky and M. Sugimoto, “Criteria for Bochner’s extension problem,” ASYMPTOTIC ANALYSIS, vol. 66, no. 3–4, pp. 125–138, 2010.
@article{8585520,
  abstract     = {{A necessary and sufficient condition for the resolution of the weak extension problem is given. This criterion is applied to also give a criterion for the solvability of the classical Bochner's extension problem in the L(p)-category. The solution of the L(p)-extension problem by Bochner [J. Math. Pures Appl. 35 (1956), 193-202] giving the relation between the order of the operator, the dimension, and index p, for which the L(p)-extension property holds, can be viewed as a subcritical case of the general L(p)-extension problem. In general, this property fails in some critical and in all supercritical cases. In this paper, the L(p)-extension problem is investigated for operators of all orders and for all 1 <= p <= infinity. Necessary and sufficient conditions on the subset of L(p) are given for which the L(p)-extension property still holds, in the critical and supercritical cases.}},
  author       = {{Ruzhansky, Michael and Sugimoto, Mitsuru}},
  issn         = {{0921-7134}},
  journal      = {{ASYMPTOTIC ANALYSIS}},
  keywords     = {{extension problem,removable singularities,PARTIAL-DIFFERENTIAL-EQUATIONS,REMOVABLE SINGULARITIES,THEOREM}},
  language     = {{eng}},
  number       = {{3-4}},
  pages        = {{125--138}},
  title        = {{Criteria for Bochner's extension problem}},
  url          = {{http://doi.org/10.3233/ASY-2009-0962}},
  volume       = {{66}},
  year         = {{2010}},
}
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