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

N.A.

Makale detayları

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

Yazarlar:

N.A.

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.1 Issue 1, pp.1-11

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001293532

pISSN:

2980-3020

Anahtar kelimeler:

Özet:

 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.

 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.

 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.

 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.

Makale detayları

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

Yazarlar:

N.A.

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.1 Issue 1, pp.1-11

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001293532

pISSN:

2980-3020

Reproducing kernel

Hardy space

Fock space

Sayı

Makale detayları

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

Yazarlar: N.A.

Yayıncı: Istanbul University

Ana Başlıklar: Pure Mathematics (Other)

Dergi: Istanbul Journal of Mathematics Vol.1 Issue 1, pp.1-11

Belge Tipi: Makale

Yayın Tarihi: 6/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001293532

pISSN: 2980-3020

Reproducing kernel

Hardy space

Fock space

Sayı

Yazarlar:

N.A.

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.1 Issue 1, pp.1-11

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001293532

pISSN:

2980-3020