uniqueness
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11: 28.7 Analytic Continuation of Eigenvalues
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►In consequence, the functions can be defined uniquely by introducing suitable cuts in the -plane.
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12: 18.40 Methods of Computation
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►Given the power moments, , , can these be used to find a unique
, a non-decreasing, real, function of , in the case that the moment problem is determined? Should a unique solution not exist the moment problem is then indeterminant.
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13: 23.3 Differential Equations
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►Given and there is a unique lattice such that (23.3.1) and (23.3.2) are satisfied.
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►Conversely, , , and the set are determined uniquely by the lattice independently of the choice of generators.
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14: 23.20 Mathematical Applications
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►There is a unique point such that .
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►For each pair of edges there is a unique point such that .
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15: 20.1 Special Notation
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, | integers. |
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the nome, , . Since is not a single-valued function of , it is assumed that is known, even when is specified. Most applications concern the rectangular case , , so that and and are uniquely related. | |
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16: 28.2 Definitions and Basic Properties
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►If , then for a given value of the corresponding Floquet solution is unique, except for an arbitrary constant factor (Theorem of Ince; see also 28.5(i)).
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►For simple roots of the corresponding equations (28.2.21) and (28.2.22), the functions are made unique by the normalizations
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17: 32.4 Isomonodromy Problems
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►Isomonodromy problems for Painlevé equations are not unique.
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18: Bibliography O
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On the uniqueness of asymptotic solutions of linear differential equations.
Methods Appl. Anal. 6 (2), pp. 165–174.
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19: 18.2 General Orthogonal Polynomials
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►The orthogonality relations (18.2.1)–(18.2.3) each determine the polynomials
uniquely up to constant factors, which may be fixed by suitable standardizations.
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§18.2(viii) Uniqueness of Orthogonality Measure and Completeness
… ►, of the form ) nor is it necessarily unique, up to a positive constant factor. However, if OP’s have an orthogonality relation on a bounded interval, then their orthogonality measure is unique, up to a positive constant factor. … ►A system of OP’s with unique orthogonality measure is always complete, see Shohat and Tamarkin (1970, Theorem 2.14). …20: 3.11 Approximation Techniques
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►Then there exists a unique
th degree polynomial , called the minimax (or best uniform) polynomial approximation to on , that minimizes , where .
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►There exists a unique solution of this minimax problem and there are at least values , , such that , where
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►is , then the approximation is determined uniquely.
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