BARGE 发表于 2025-3-26 23:38:44
978-3-0348-9459-3Springer Basel AG 2002Spinal-Tap 发表于 2025-3-27 01:21:02
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https://doi.org/10.1007/978-3-0348-8155-5Boundary value problem; Differential equations; Hilbert space; differential equation; orthogonal polynomCAND 发表于 2025-3-27 11:28:53
Bounded Linear Operators On a Hilbert SpaceEveryone is familiar with linear operators. Multiplication by a constant is a linear operator. Multiplication of vectors by matrices generates an operator. Integration usually generates another, depending upon the setting.社团 发表于 2025-3-27 17:22:45
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Hinton and Shaw’s Extension of Weyl’s M (λ) Theory to SystemsD. B. Hinton and J. K. Shaw have developed an extension of the Weyl theory which is a bit different from that of Chapter VI, and which proves to be ultimately much more useful in deriving the spectral resolution for self-adjoint systems.解脱 发表于 2025-3-27 22:15:49
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DistributionsOur goal in the near future is to find and catagorize those boundary value problems which have orthogonal polynomial solutions, but first we must define what we mean by “orthogonal polynomials,” and in order to do so we need some concepts from the theory of distributions.pessimism 发表于 2025-3-28 09:56:23
Orthogonal PolynomialsWe plan to examine collections of orthogonal polynomials satisfying second, fourth and higher order differential equations in detail. However, since they have a great deal in common, we develop that common ground here.obstruct 发表于 2025-3-28 10:25:18
Orthogonal Polynomials Satisfying Sixth Order Differential EquationsWe remind the reader that every even ordered formally symmetric differential operator can be rewritten as a real symmetric linear Hamiltonian system.