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

H. Turgay Kaptanoğlu

Makale detayları

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

Yazarlar:

H. Turgay Kaptanoğlu

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.1 Issue 1, pp.12-19

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001293533

pISSN:

2980-3020

Anahtar kelimeler:

Özet:

 On weighted Bergman and Hardy Hilbert spaces on the unit ball of the complex -space, we consider weighted compositon operators  in which the composition is by an automorphism  of the unit ball and the weight is a power of the Jacobian of  in such a way that the operator is unitary. Assuming that the homogeneous expansion of an  in one of these spaces contains only terms with total degree even odd, respectively and the homogeneous expansion of   contains only terms with total degree odd even, respectively, we prove that  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.

 On weighted Bergman and Hardy Hilbert spaces on the unit ball of the complex -space, we consider weighted compositon operators  in which the composition is by an automorphism  of the unit ball and the weight is a power of the Jacobian of  in such a way that the operator is unitary. Assuming that the homogeneous expansion of an  in one of these spaces contains only terms with total degree even odd, respectively and the homogeneous expansion of   contains only terms with total degree odd even, respectively, we prove that  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.

 On weighted Bergman and Hardy Hilbert spaces on the unit ball of the complex -space, we consider weighted compositon operators  in which the composition is by an automorphism  of the unit ball and the weight is a power of the Jacobian of  in such a way that the operator is unitary. Assuming that the homogeneous expansion of an  in one of these spaces contains only terms with total degree even odd, respectively and the homogeneous expansion of   contains only terms with total degree odd even, respectively, we prove that  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.

 On weighted Bergman and Hardy Hilbert spaces on the unit ball of the complex -space, we consider weighted compositon operators  in which the composition is by an automorphism  of the unit ball and the weight is a power of the Jacobian of  in such a way that the operator is unitary. Assuming that the homogeneous expansion of an  in one of these spaces contains only terms with total degree even odd, respectively and the homogeneous expansion of   contains only terms with total degree odd even, respectively, we prove that  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.

Makale detayları

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

Yazarlar:

H. Turgay Kaptanoğlu

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.1 Issue 1, pp.12-19

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001293533

pISSN:

2980-3020

Weighted composition operator

unitary operator

Bergman-Besov space

Hardy space

Dirichlet space

Drury-Arveson space

Sayı

Makale detayları

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

Yazarlar: H. Turgay Kaptanoğlu

Yayıncı: Istanbul University

Ana Başlıklar: Pure Mathematics (Other)

Dergi: Istanbul Journal of Mathematics Vol.1 Issue 1, pp.12-19

Belge Tipi: Makale

Yayın Tarihi: 6/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001293533

pISSN: 2980-3020

Weighted composition operator

unitary operator

Bergman-Besov space

Hardy space

Dirichlet space

Drury-Arveson space

Sayı

Yazarlar:

H. Turgay Kaptanoğlu

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.1 Issue 1, pp.12-19

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001293533

pISSN:

2980-3020