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ANALYSIS OF CONTINUOUS FRAMES BY TRANSFERRING TO DISCRITE FRAMES | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 آبان 1402 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2023.66029.2228 | ||
| نویسندگان | ||
Reihaneh Raisi Tousi  1؛ Rajabali Kamyabi gol2؛ Hoseyn AVAZZADEH2؛ Atefe Razghandi3
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| 1Ferdowsi university of mashhad | ||
| 2Department of Mathematics, Ferdowsi University of Mashhad | ||
| 3Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran | ||
| چکیده | ||
| .In this paper we characterize continuous Riesz bases and give some of their relations with continuous orthonormal bases that are well known in the discrete frame setting. We also give necessary conditions for a continuous frame to be a continuous Riesz basis or a continuous orthonormal basis. Especially, we show that every continuous Riesz basis is the (weak) image of a continuous orthonormal basis via a bounded invertible operator.We show that continuous frames act very similar to discrete frames, In fact there is a correspondence between continuous and discrete frames. As an application, one can solve several problems in continuous frames with the aid of discrete frames. We give some relations between continuous and discrete frames. In particular, we define and then characterize exact continuous frames via continuous Riesz bases and show that continuous exact frames are exactly continuous Riesz bases. Finally, we characterize alternate dual of continuous frames by transferring the problem to discrete frames and using discrete dual frames | ||
| کلیدواژهها | ||
| Continuous Riesz basis؛ continuous orthonormal basis؛ Riesz basis؛ continuous frame | ||
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آمار تعداد مشاهده مقاله: 14 |
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