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It is proved that if the increasing sequence kn n=0..∞
n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply
connected subregion of CRthen the system of Hermite associated functions
Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.
Rusev, Peter. "Complete Systems of Hermite Associated Functions." Serdica Mathematical Journal 26.3 (2000): 221-228. <http://eudml.org/doc/11490>.
@article{Rusev2000, abstract = {It is proved that if the increasing sequence kn n=0..∞
n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply
connected subregion of CRthen the system of Hermite associated functions
Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.}, author = {Rusev, Peter}, journal = {Serdica Mathematical Journal}, keywords = {Hermite Polynomials; Hermite Associated Functions; Completeness; Hermite polynomials; Hermite associated functions; completeness}, language = {eng}, number = {3}, pages = {221-228}, publisher = {Institute of Mathematics and Informatics}, title = {Complete Systems of Hermite Associated Functions}, url = {http://eudml.org/doc/11490}, volume = {26}, year = {2000}, }
TY - JOUR AU - Rusev, Peter TI - Complete Systems of Hermite Associated Functions JO - Serdica Mathematical Journal PY - 2000 PB - Institute of Mathematics and Informatics VL - 26 IS - 3 SP - 221 EP - 228 AB - It is proved that if the increasing sequence kn n=0..∞
n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply
connected subregion of CRthen the system of Hermite associated functions
Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D. LA - eng KW - Hermite Polynomials; Hermite Associated Functions; Completeness; Hermite polynomials; Hermite associated functions; completeness UR - http://eudml.org/doc/11490 ER -