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Sums of A Pair of Orthogonal Frames
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| Zeitschriftentitel: | Mathematics |
|---|---|
| Personen und Körperschaften: | |
| In: | Mathematics, 7, 2019, 7, S. 582 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
MDPI AG
|
| Schlagwörter: |
| author_facet |
Bhatt, Ghanshyam Bhatt, Ghanshyam |
|---|---|
| author |
Bhatt, Ghanshyam |
| spellingShingle |
Bhatt, Ghanshyam Mathematics Sums of A Pair of Orthogonal Frames General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) |
| author_sort |
bhatt, ghanshyam |
| spelling |
Bhatt, Ghanshyam 2227-7390 MDPI AG General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) http://dx.doi.org/10.3390/math7070582 <jats:p>Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames.</jats:p> Sums of A Pair of Orthogonal Frames Mathematics |
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MDPI AG, 2019 |
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MDPI AG, 2019 |
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Mathematics |
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49 |
| title |
Sums of A Pair of Orthogonal Frames |
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Sums of A Pair of Orthogonal Frames |
| title_full |
Sums of A Pair of Orthogonal Frames |
| title_fullStr |
Sums of A Pair of Orthogonal Frames |
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Sums of A Pair of Orthogonal Frames |
| title_short |
Sums of A Pair of Orthogonal Frames |
| title_sort |
sums of a pair of orthogonal frames |
| topic |
General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) |
| url |
http://dx.doi.org/10.3390/math7070582 |
| publishDate |
2019 |
| physical |
582 |
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<jats:p>Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames.</jats:p> |
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| description | <jats:p>Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames.</jats:p> |
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| imprint | MDPI AG, 2019 |
| imprint_str_mv | MDPI AG, 2019 |
| institution | DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161 |
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| series | Mathematics |
| source_id | 49 |
| spelling | Bhatt, Ghanshyam 2227-7390 MDPI AG General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) http://dx.doi.org/10.3390/math7070582 <jats:p>Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames.</jats:p> Sums of A Pair of Orthogonal Frames Mathematics |
| spellingShingle | Bhatt, Ghanshyam, Mathematics, Sums of A Pair of Orthogonal Frames, General Mathematics, Engineering (miscellaneous), Computer Science (miscellaneous) |
| title | Sums of A Pair of Orthogonal Frames |
| title_full | Sums of A Pair of Orthogonal Frames |
| title_fullStr | Sums of A Pair of Orthogonal Frames |
| title_full_unstemmed | Sums of A Pair of Orthogonal Frames |
| title_short | Sums of A Pair of Orthogonal Frames |
| title_sort | sums of a pair of orthogonal frames |
| title_unstemmed | Sums of A Pair of Orthogonal Frames |
| topic | General Mathematics, Engineering (miscellaneous), Computer Science (miscellaneous) |
| url | http://dx.doi.org/10.3390/math7070582 |