Abstract
Suppose thatD={z:|z|<1}, L 2 (D) is the space of functions square-integrable over area inD,A k (D) is the set of allk-analytic functions inD, (A 1 (D)=A(D) is the set of all analytic functions inD),A k L 2 (D)=L 2 (D)∩A k (D),A 1 L 2 (D)=AL 2 (D),
. It is proved that the subspacesA k L 02 (D),k=1, 2,..., are orthogonal to one another and the spaceA m L 2 (D) is the direct sum of such subspaces fork=1, 2,...,m. The kernel of the orthogonal projection operator from the spaceA m L 2 (D) onto its subspacesA k L 02 (D) is obtained. These results are applied to the study of the properties of polyrational functions of best approximation in the metricL 2 (D).
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Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 741–759, November, 1999.
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Ramazanov, A.K. Representation of the space of polyanalytic functions as a direct sum of orthogonal subspaces. Application to rational approximations. Math Notes 66, 613–627 (1999). https://doi.org/10.1007/BF02674203
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DOI: https://doi.org/10.1007/BF02674203