Concavity of some operator functions and Fréchet differential mappings
By using operator perspectives of regular operator mappings we obtain some operator concave (convex) functions and derive the concavity (convexity) of some trace functions associated with the Fréchet differential mapping of certain power functions. Especially, we explore the concavity of the Fréchet...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Shi, Guanghua [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Umfang: |
11 |
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| Übergeordnetes Werk: |
Enthalten in: CFD investigation on particle deposition in aligned and staggered ribbed duct air flows - Lu, Hao ELSEVIER, 2016, LAA, New York, NY |
|---|---|
| Übergeordnetes Werk: |
volume:590 ; year:2020 ; day:1 ; month:04 ; pages:224-234 ; extent:11 |
| Links: |
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| DOI / URN: |
10.1016/j.laa.2019.12.031 |
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| 520 | |a By using operator perspectives of regular operator mappings we obtain some operator concave (convex) functions and derive the concavity (convexity) of some trace functions associated with the Fréchet differential mapping of certain power functions. Especially, we explore the concavity of the Fréchet differential mapping x → d g ( x ) ⁎ d f ( x ) − 1 in positive definite invertible operators with f ( t ) = t p for 0 < p ≤ 1 and g ( t ) = t q for p ≤ q ≤ p + 1 , and also with f ( t ) = log t and g ( t ) = t q for 0 < q ≤ 1 . | ||
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10.1016/j.laa.2019.12.031 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000898.pica (DE-627)ELV04926768X (ELSEVIER)S0024-3795(19)30545-2 DE-627 ger DE-627 rakwb eng 690 VZ 530 620 VZ 52.56 bkl Shi, Guanghua verfasserin aut Concavity of some operator functions and Fréchet differential mappings 2020 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier By using operator perspectives of regular operator mappings we obtain some operator concave (convex) functions and derive the concavity (convexity) of some trace functions associated with the Fréchet differential mapping of certain power functions. Especially, we explore the concavity of the Fréchet differential mapping x → d g ( x ) ⁎ d f ( x ) − 1 in positive definite invertible operators with f ( t ) = t p for 0 < p ≤ 1 and g ( t ) = t q for p ≤ q ≤ p + 1 , and also with f ( t ) = log t and g ( t ) = t q for 0 < q ≤ 1 . 47A05 Elsevier 47A64 Elsevier 47A60 Elsevier Enthalten in American Elsevier Publ Lu, Hao ELSEVIER CFD investigation on particle deposition in aligned and staggered ribbed duct air flows 2016 LAA New York, NY (DE-627)ELV014483130 volume:590 year:2020 day:1 month:04 pages:224-234 extent:11 https://doi.org/10.1016/j.laa.2019.12.031 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 GBV_ILN_2015 GBV_ILN_2021 52.56 Regenerative Energieformen alternative Energieformen VZ AR 590 2020 1 0401 224-234 11 |
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By using operator perspectives of regular operator mappings we obtain some operator concave (convex) functions and derive the concavity (convexity) of some trace functions associated with the Fréchet differential mapping of certain power functions. Especially, we explore the concavity of the Fréchet differential mapping x → d g ( x ) ⁎ d f ( x ) − 1 in positive definite invertible operators with f ( t ) = t p for 0 < p ≤ 1 and g ( t ) = t q for p ≤ q ≤ p + 1 , and also with f ( t ) = log t and g ( t ) = t q for 0 < q ≤ 1 . |
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By using operator perspectives of regular operator mappings we obtain some operator concave (convex) functions and derive the concavity (convexity) of some trace functions associated with the Fréchet differential mapping of certain power functions. Especially, we explore the concavity of the Fréchet differential mapping x → d g ( x ) ⁎ d f ( x ) − 1 in positive definite invertible operators with f ( t ) = t p for 0 < p ≤ 1 and g ( t ) = t q for p ≤ q ≤ p + 1 , and also with f ( t ) = log t and g ( t ) = t q for 0 < q ≤ 1 . |
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By using operator perspectives of regular operator mappings we obtain some operator concave (convex) functions and derive the concavity (convexity) of some trace functions associated with the Fréchet differential mapping of certain power functions. Especially, we explore the concavity of the Fréchet differential mapping x → d g ( x ) ⁎ d f ( x ) − 1 in positive definite invertible operators with f ( t ) = t p for 0 < p ≤ 1 and g ( t ) = t q for p ≤ q ≤ p + 1 , and also with f ( t ) = log t and g ( t ) = t q for 0 < q ≤ 1 . |
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Concavity of some operator functions and Fréchet differential mappings |
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