# A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform

Bent Ørsted^{[1]}; Jorge Vargas^{[2]}

- [1] Ny Munkegade Department of Mathematics 8000 Aarhus C. (Danemark)
- [2] Universidad Nacional de Córdoba FAMAF-CIEM Ciudad Universitaria 5000 Córdoba (Argentine)

Annales de l’institut Fourier (2007)

- Volume: 57, Issue: 3, page 693-702
- ISSN: 0373-0956

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topØrsted, Bent, and Vargas, Jorge. "A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform." Annales de l’institut Fourier 57.3 (2007): 693-702. <http://eudml.org/doc/10237>.

@article{Ørsted2007,

abstract = {In this note, we generalize the results in our previous paper on the Casimir operator and Berezin transform, by showing the $(L^2,L^2)$-continuity of a generalized Berezin transform associated with a branching problem for a class of unitary representations defined by invariant elliptic operators; we also show, that under suitable general conditions, this generalized Berezin transform is $(L^p, L^p)$-continuous for $ 1 \le p \le \infty .$},

affiliation = {Ny Munkegade Department of Mathematics 8000 Aarhus C. (Danemark); Universidad Nacional de Córdoba FAMAF-CIEM Ciudad Universitaria 5000 Córdoba (Argentine)},

author = {Ørsted, Bent, Vargas, Jorge},

journal = {Annales de l’institut Fourier},

keywords = {Discrete Series representations; branching laws; invariant elliptic operators; Berezin transform; unitary representation; Casimir operator; semisimple Lie group},

language = {eng},

number = {3},

pages = {693-702},

publisher = {Association des Annales de l’institut Fourier},

title = {A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform},

url = {http://eudml.org/doc/10237},

volume = {57},

year = {2007},

}

TY - JOUR

AU - Ørsted, Bent

AU - Vargas, Jorge

TI - A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform

JO - Annales de l’institut Fourier

PY - 2007

PB - Association des Annales de l’institut Fourier

VL - 57

IS - 3

SP - 693

EP - 702

AB - In this note, we generalize the results in our previous paper on the Casimir operator and Berezin transform, by showing the $(L^2,L^2)$-continuity of a generalized Berezin transform associated with a branching problem for a class of unitary representations defined by invariant elliptic operators; we also show, that under suitable general conditions, this generalized Berezin transform is $(L^p, L^p)$-continuous for $ 1 \le p \le \infty .$

LA - eng

KW - Discrete Series representations; branching laws; invariant elliptic operators; Berezin transform; unitary representation; Casimir operator; semisimple Lie group

UR - http://eudml.org/doc/10237

ER -

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