New aspects of weaving K-frames: the excess and duality

Ali Akbar Arefijamaal

Makale detayları

New aspects of weaving K-frames: the excess and duality

Yazarlar:

Ali Akbar Arefijamaal

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 3, pp.652-666

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001320018

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K -frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a K-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.

 Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K -frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a K-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.

 Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K -frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a K-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.

 Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K -frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a K-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.

Makale detayları

New aspects of weaving K-frames: the excess and duality

Yazarlar:

Ali Akbar Arefijamaal

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 3, pp.652-666

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001320018

pISSN:

2651-477X

frames

dual frames

Riesz bases

woven frames

excess of frames

K-frames

Sayı

Makale detayları

New aspects of weaving K-frames: the excess and duality

Yazarlar: Ali Akbar Arefijamaal

Yayıncı: Hacettepe University

Ana Başlıklar: Mathematical Sciences

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 3, pp.652-666

Belge Tipi: Makale

Yayın Tarihi: 6/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001320018

pISSN: 2651-477X

frames

dual frames

Riesz bases

woven frames

excess of frames

K-frames

Sayı

Yazarlar:

Ali Akbar Arefijamaal

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 3, pp.652-666

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001320018

pISSN:

2651-477X