Research Article


DOI :10.26650/ijmath.2023.00004   IUP :10.26650/ijmath.2023.00004    Full Text (PDF)

Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball

Hakkı Turgay Kaptanoğlu

On weighted Bergman and Hardy Hilbert spaces on the unit ball of the complex 𝑁-space, we consider weighted compositon operators 𝑇𝜓 in which the composition is by an automorphism 𝜓 of the unit ball and the weight is a power of the Jacobian of 𝜓 in such a way that the operator is unitary. Assuming that the homogeneous expansion of an 𝑓 in one of these spaces contains only terms with total degree even (odd, respectively) and the homogeneous expansion of 𝑇𝜓 𝑓 contains only terms with total degree odd (even, respectively), we prove that 𝑓 is the zero function. We also find related operators on the remaining Bergman-Besov Hilbert spaces including the Drury-Arveson space and the Dirichlet space for which the same result holds. Our results generalize the results obtained in Montes-Rodríguez (2023) on three function spaces on the unit disc to a wider family of function spaces on the unit ball.


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References

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APA

Kaptanoğlu, H.T. (2023). Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball. Istanbul Journal of Mathematics, 1(1), 12-19. https://doi.org/10.26650/ijmath.2023.00004


AMA

Kaptanoğlu H T. Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball. Istanbul Journal of Mathematics. 2023;1(1):12-19. https://doi.org/10.26650/ijmath.2023.00004


ABNT

Kaptanoğlu, H.T. Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball. Istanbul Journal of Mathematics, [Publisher Location], v. 1, n. 1, p. 12-19, 2023.


Chicago: Author-Date Style

Kaptanoğlu, Hakkı Turgay,. 2023. “Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball.” Istanbul Journal of Mathematics 1, no. 1: 12-19. https://doi.org/10.26650/ijmath.2023.00004


Chicago: Humanities Style

Kaptanoğlu, Hakkı Turgay,. Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball.” Istanbul Journal of Mathematics 1, no. 1 (Jul. 2024): 12-19. https://doi.org/10.26650/ijmath.2023.00004


Harvard: Australian Style

Kaptanoğlu, HT 2023, 'Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball', Istanbul Journal of Mathematics, vol. 1, no. 1, pp. 12-19, viewed 23 Jul. 2024, https://doi.org/10.26650/ijmath.2023.00004


Harvard: Author-Date Style

Kaptanoğlu, H.T. (2023) ‘Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball’, Istanbul Journal of Mathematics, 1(1), pp. 12-19. https://doi.org/10.26650/ijmath.2023.00004 (23 Jul. 2024).


MLA

Kaptanoğlu, Hakkı Turgay,. Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball.” Istanbul Journal of Mathematics, vol. 1, no. 1, 2023, pp. 12-19. [Database Container], https://doi.org/10.26650/ijmath.2023.00004


Vancouver

Kaptanoğlu HT. Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball. Istanbul Journal of Mathematics [Internet]. 23 Jul. 2024 [cited 23 Jul. 2024];1(1):12-19. Available from: https://doi.org/10.26650/ijmath.2023.00004 doi: 10.26650/ijmath.2023.00004


ISNAD

Kaptanoğlu, HakkıTurgay. Unitary weighted composition operators on Bergman-Besov and Hardy Hilbert spaces on the ball”. Istanbul Journal of Mathematics 1/1 (Jul. 2024): 12-19. https://doi.org/10.26650/ijmath.2023.00004



TIMELINE


Submitted17.05.2023
Accepted01.06.2023
Published Online12.06.2023

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