DEB, Prahllad a Somnath HAZRA. A family of homogeneous operators in the Cowen-Douglas class over the poly-disc. Studia Mathematica. Warsaw, Poland: IMPAN - Institute of Mathematics. Polish Academy of Sciences, 2023, roč. 271, č. 1, s. 65-84. ISSN 0039-3223. Dostupné z: https://dx.doi.org/10.4064/sm220630-10-1. |
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@article{78326, author = {Deb, Prahllad and Hazra, Somnath}, article_location = {Warsaw, Poland}, article_number = {1}, doi = {http://dx.doi.org/10.4064/sm220630-10-1}, keywords = {Cowen-Douglas class; curvature; hermitian holomorphic homogeneous vector bundles; homogeneous operators}, language = {eng}, issn = {0039-3223}, journal = {Studia Mathematica}, title = {A family of homogeneous operators in the Cowen-Douglas class over the poly-disc}, url = {https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/271/1/115001/a-family-of-homogeneous-operators-in-the-cowen-douglas-class-over-the-poly-disc}, volume = {271}, year = {2023} }
TY - JOUR ID - 78326 AU - Deb, Prahllad - Hazra, Somnath PY - 2023 TI - A family of homogeneous operators in the Cowen-Douglas class over the poly-disc JF - Studia Mathematica VL - 271 IS - 1 SP - 65-84 EP - 65-84 PB - IMPAN - Institute of Mathematics. Polish Academy of Sciences SN - 00393223 KW - Cowen-Douglas class KW - curvature KW - hermitian holomorphic homogeneous vector bundles KW - homogeneous operators UR - https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/271/1/115001/a-family-of-homogeneous-operators-in-the-cowen-douglas-class-over-the-poly-disc N2 - We construct a large family of positive definite kernels K : Dn x Dn-+ M(r, C), holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the subgroup Mob x center dot center dot center dot x Mob (n times) of the bi-holomorphic automorphism group of Dn. The adjoint of the n-tuple of the multiplication operators by the co-ordinate functions is then homogeneous with respect to this subgroup on the Hilbert space ?-lK determined by K. We show that these n-tuples are irreducible, are in the Cowen-Douglas class Br(Dn) and are mutually pairwise unitarily inequivalent. ER -
DEB, Prahllad a Somnath HAZRA. A family of homogeneous operators in the Cowen-Douglas class over the poly-disc. \textit{Studia Mathematica}. Warsaw, Poland: IMPAN - Institute of Mathematics. Polish Academy of Sciences, 2023, roč.~271, č.~1, s.~65-84. ISSN~0039-3223. Dostupné z: https://dx.doi.org/10.4064/sm220630-10-1.
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