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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Euler spaces of analytic functions


Author: James Rovnyak
Journal: Trans. Amer. Math. Soc. 308 (1988), 197-208
MSC: Primary 30H05; Secondary 44A15, 46E20
MathSciNet review: 929669
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Abstract: A formula due to Euler and Legendre is used to construct finite-difference counterparts to the Dirichlet space. The spaces have integral representations and characterizations in terms of area integrals. Their reproducing kernels are logarithms of the reproducing kernels of the Newton spaces, which are counterparts to the Hardy class. A Hilbert space with reproducing kernel

$\displaystyle \log [(1/\overline w z)\,\log \;1/(1 - \overline w z)]$

is also shown to exist and to be related to Bernoulli numbers and combinatorial theory.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0929669-9
PII: S 0002-9947(1988)0929669-9
Article copyright: © Copyright 1988 American Mathematical Society