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DOI :10.26650/ijmath.2023.00005   IUP :10.26650/ijmath.2023.00005    Full Text (PDF)

A new characterization of the Hardy space and of other Hilbert spaces of analytic functions

Natanael Alpay

The Fock space can be characterized (up to a positive multiplicative factor) as the only Hilbert space of entire functions in which the adjoint of derivation is multiplication by the complex variable. Similarly (and still up to a positive multiplicative factor) the Hardy space is the only space of functions analytic in the open unit disk for which the adjoint of the backward shift operator is the multiplication operator. In the present paper we characterize the Hardy space and some related reproducing kernel Hilbert spaces in terms of the adjoint of the differentiation operator. We use reproducing kernel methods, which seem to also give a new characterization of the Fock space. 

Keywords: Reproducing kernel, Hardy space, Fock space

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References

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APA

Alpay, N. (2023). A new characterization of the Hardy space and of other Hilbert spaces of analytic functions. Istanbul Journal of Mathematics, 1(1), 1-11. https://doi.org/10.26650/ijmath.2023.00005


AMA

Alpay N. A new characterization of the Hardy space and of other Hilbert spaces of analytic functions. Istanbul Journal of Mathematics. 2023;1(1):1-11. https://doi.org/10.26650/ijmath.2023.00005


ABNT

Alpay, N. A new characterization of the Hardy space and of other Hilbert spaces of analytic functions. Istanbul Journal of Mathematics, [Publisher Location], v. 1, n. 1, p. 1-11, 2023.


Chicago: Author-Date Style

Alpay, Natanael,. 2023. “A new characterization of the Hardy space and of other Hilbert spaces of analytic functions.” Istanbul Journal of Mathematics 1, no. 1: 1-11. https://doi.org/10.26650/ijmath.2023.00005


Chicago: Humanities Style

Alpay, Natanael,. “A new characterization of the Hardy space and of other Hilbert spaces of analytic functions.” Istanbul Journal of Mathematics 1, no. 1 (Sep. 2023): 1-11. https://doi.org/10.26650/ijmath.2023.00005


Harvard: Australian Style

Alpay, N 2023, 'A new characterization of the Hardy space and of other Hilbert spaces of analytic functions', Istanbul Journal of Mathematics, vol. 1, no. 1, pp. 1-11, viewed 21 Sep. 2023, https://doi.org/10.26650/ijmath.2023.00005


Harvard: Author-Date Style

Alpay, N. (2023) ‘A new characterization of the Hardy space and of other Hilbert spaces of analytic functions’, Istanbul Journal of Mathematics, 1(1), pp. 1-11. https://doi.org/10.26650/ijmath.2023.00005 (21 Sep. 2023).


MLA

Alpay, Natanael,. “A new characterization of the Hardy space and of other Hilbert spaces of analytic functions.” Istanbul Journal of Mathematics, vol. 1, no. 1, 2023, pp. 1-11. [Database Container], https://doi.org/10.26650/ijmath.2023.00005


Vancouver

Alpay N. A new characterization of the Hardy space and of other Hilbert spaces of analytic functions. Istanbul Journal of Mathematics [Internet]. 21 Sep. 2023 [cited 21 Sep. 2023];1(1):1-11. Available from: https://doi.org/10.26650/ijmath.2023.00005 doi: 10.26650/ijmath.2023.00005


ISNAD

Alpay, Natanael. “A new characterization of the Hardy space and of other Hilbert spaces of analytic functions”. Istanbul Journal of Mathematics 1/1 (Sep. 2023): 1-11. https://doi.org/10.26650/ijmath.2023.00005



TIMELINE


Submitted28.03.2023
Accepted16.06.2023
Published Online19.06.2023

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