Stability Theorems in Geometry and Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1994
|
| Schriftenreihe: | Mathematics and Its Applications
304 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. • Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X},X2,'" ,xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR. , i.e., for x = (Xl, X2, •.• , xn) and y = (y}, Y2,··., Yn), Ixl = Jx~ + x~ + ... + x~, (x, y) = XIYl + X2Y2 + ... + XnYn. n Given arbitrary points a and b in lR. , we denote by [a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form x = >.a + I'b, where>. + I' = 1 and >. ~ 0, I' ~ O. n We denote by ei, i = 1,2, ... ,n, the vector in lR. whose ith coordinate is equal to 1 and the others vanish. The vectors el, e2, ... ,en form a basis for the space n lR. , which is called canonical. If P( x) is some proposition in a variable x and A is a set, then {x E A I P(x)} denotes the collection of all the elements of A for which the proposition P( x) is true |
| Beschreibung: | 1 Online-Ressource (XII, 394 p) |
| ISBN: | 9789401583602 9789048144679 |
| DOI: | 10.1007/978-94-015-8360-2 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804153100527730688 |
|---|---|
| any_adam_object | |
| author | Reshetnyak, Yu. G. |
| author_facet | Reshetnyak, Yu. G. |
| author_role | aut |
| author_sort | Reshetnyak, Yu. G. |
| author_variant | y g r yg ygr |
| building | Verbundindex |
| bvnumber | BV042424051 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184501759 (DE-599)BVBBV042424051 |
| dewey-full | 515.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.72 |
| dewey-search | 515.72 |
| dewey-sort | 3515.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8360-2 |
| format | Electronic eBook |
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| id | DE-604.BV042424051 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401583602 9789048144679 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859468 |
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| physical | 1 Online-Ressource (XII, 394 p) |
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| publishDate | 1994 |
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| publisher | Springer Netherlands |
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| series2 | Mathematics and Its Applications |
| spelling | Reshetnyak, Yu. G. Verfasser aut Stability Theorems in Geometry and Analysis by Yu. G. Reshetnyak Dordrecht Springer Netherlands 1994 1 Online-Ressource (XII, 394 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 304 1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. • Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X},X2,'" ,xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR. , i.e., for x = (Xl, X2, •.• , xn) and y = (y}, Y2,··., Yn), Ixl = Jx~ + x~ + ... + x~, (x, y) = XIYl + X2Y2 + ... + XnYn. n Given arbitrary points a and b in lR. , we denote by [a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form x = >.a + I'b, where>. + I' = 1 and >. ~ 0, I' ~ O. n We denote by ei, i = 1,2, ... ,n, the vector in lR. whose ith coordinate is equal to 1 and the others vanish. The vectors el, e2, ... ,en form a basis for the space n lR. , which is called canonical. If P( x) is some proposition in a variable x and A is a set, then {x E A I P(x)} denotes the collection of all the elements of A for which the proposition P( x) is true Mathematics Topological Groups Integral equations Integral Transforms Geometry Mathematical optimization Integral Transforms, Operational Calculus Integral Equations Calculus of Variations and Optimal Control; Optimization Topological Groups, Lie Groups Mathematik Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Liouville-Satz (DE-588)4167786-9 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 s Liouville-Satz (DE-588)4167786-9 s Stabilität (DE-588)4056693-6 s 1\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 2\p DE-604 https://doi.org/10.1007/978-94-015-8360-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Reshetnyak, Yu. G. Stability Theorems in Geometry and Analysis Mathematics Topological Groups Integral equations Integral Transforms Geometry Mathematical optimization Integral Transforms, Operational Calculus Integral Equations Calculus of Variations and Optimal Control; Optimization Topological Groups, Lie Groups Mathematik Konforme Abbildung (DE-588)4164968-0 gnd Liouville-Satz (DE-588)4167786-9 gnd Stabilität (DE-588)4056693-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4164968-0 (DE-588)4167786-9 (DE-588)4056693-6 (DE-588)4012248-7 |
| title | Stability Theorems in Geometry and Analysis |
| title_auth | Stability Theorems in Geometry and Analysis |
| title_exact_search | Stability Theorems in Geometry and Analysis |
| title_full | Stability Theorems in Geometry and Analysis by Yu. G. Reshetnyak |
| title_fullStr | Stability Theorems in Geometry and Analysis by Yu. G. Reshetnyak |
| title_full_unstemmed | Stability Theorems in Geometry and Analysis by Yu. G. Reshetnyak |
| title_short | Stability Theorems in Geometry and Analysis |
| title_sort | stability theorems in geometry and analysis |
| topic | Mathematics Topological Groups Integral equations Integral Transforms Geometry Mathematical optimization Integral Transforms, Operational Calculus Integral Equations Calculus of Variations and Optimal Control; Optimization Topological Groups, Lie Groups Mathematik Konforme Abbildung (DE-588)4164968-0 gnd Liouville-Satz (DE-588)4167786-9 gnd Stabilität (DE-588)4056693-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Mathematics Topological Groups Integral equations Integral Transforms Geometry Mathematical optimization Integral Transforms, Operational Calculus Integral Equations Calculus of Variations and Optimal Control; Optimization Topological Groups, Lie Groups Mathematik Konforme Abbildung Liouville-Satz Stabilität Differentialgeometrie |
| url | https://doi.org/10.1007/978-94-015-8360-2 |
| work_keys_str_mv | AT reshetnyakyug stabilitytheoremsingeometryandanalysis |