Meixner and Pollaczek spaces of entire functions

Branges, Louis de; Trutt, David

doi:10.1016/0022-247x(68)90156-x

Cited by 35 publications

(5 citation statements)

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“…Since D is selfadjoint, the identity (tF(t -l),Git)) = a*(F(t),G(t + 1)) holds whenever F(2) and G(2) belong to the domain of multiplication by 2 in the space. As in the proof of Theorem 1 of [2], this implies that L+ acts as a bounded transformation on the domain of multiplication by 2. Since the action of D+aL++aL^ coincides with multiplication by 2, multiplication by 2 is a bounded transformation in the space.…”

Section: It Follows That the Identity (Tfit -1) -A2f(¿ + 1) G(0> = -mentioning

confidence: 79%

“…These spaces, like those of previous work [2], are related to generalized spaces of square summable power series. Let a and c he numbers such that the coefficients of Rummer's series Fia; c; z) are all positive.…”

Section: Theoremmentioning

confidence: 99%

“…Since the action of D+aL++aL^ coincides with multiplication by 2, multiplication by 2 is a bounded transformation in the space. An argument in the proof of Theorem 1 of [2] will show that the space is finite dimensional.…”

Section: It Follows That the Identity (Tfit -1) -A2f(¿ + 1) G(0> = -mentioning

confidence: 99%

“…Let 3C(£) be the set of entire functions £(2) such that /+00 |f(/)/£(0|2^ < °°-cc and such that |f(2)|2^||f||2a (2,2) for all complex 2. Then X(£) is a Hilbert space of entire functions which satisfies the axioms (HI), (H2), and (H3).…”

Section: K(wz) = [B(z)l(w) -A(z)bíw)]/[tt(z -W)]mentioning

confidence: 99%

“…If £ (2) is such a function, we write £(2) = Aiz) -iB(z) where Aiz) and 73 (2) are entire functions which are real for real 2, and…”

mentioning

confidence: 99%

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Charlier spaces of entire functions

Branges¹,

Trutt²

1969

Proc. Amer. Math. Soc.

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Section: It Follows That the Identity (Tfit -1) -A2f(¿ + 1) G(0> = -mentioning

confidence: 79%

Section: Theoremmentioning

confidence: 99%

Section: It Follows That the Identity (Tfit -1) -A2f(¿ + 1) G(0> = -mentioning

confidence: 99%

Section: K(wz) = [B(z)l(w) -A(z)bíw)]/[tt(z -W)]mentioning

confidence: 99%

“…If £ (2) is such a function, we write £(2) = Aiz) -iB(z) where Aiz) and 73 (2) are entire functions which are real for real 2, and…”

mentioning

confidence: 99%

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Charlier spaces of entire functions

Branges¹,

Trutt²

1969

Proc. Amer. Math. Soc.

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Regular Sturm ‐ Liouville Problems Whose Coefficients Depend Rationally on the Eigenvalue Parameter

Snoo¹

1996

Mathematische Nachrichten

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In this note we consider regular Sturm -Liouville equations with a floating singularity of a special type: the coefficient of the second order derivative contains the eigenvalue parameter. We determine the form of the boundary conditions which make the problem selfadjoint after linearizing. In general the boundary conditions for the linearized system give rise to boundary conditions which involve the eigenvalue parameter in the original, non -linearized, problem. The boundary conditions give rise to a 2 x 2 matrix function, the so-called Titchmarsh-Weyl coefficient. The characteristic properties of this function are studied. The formal aspects of the theory of this class of equations turn out to be quite parallel to those for the usual situation when there is no floating singularity.

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Discrete canonical system and non‐Abelian Toda lattice: Bäcklund–Darboux transformation, Weyl functions, and explicit solutions

Sakhnovich

2007

Mathematische Nachrichten

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A version of the iterated Bäcklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete canonical system and Non-Abelian Toda lattice. Results on the transformations of the Weyl functions, insertion of the eigenvalues, and construction of the bound states are obtained. A wide class of the explicit solutions is given. An application to the semi-infinite block Jacobi matrices is treated.

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Meixner and Pollaczek spaces of entire functions

Cited by 35 publications

References 1 publication

Charlier spaces of entire functions

Charlier spaces of entire functions

Regular Sturm ‐ Liouville Problems Whose Coefficients Depend Rationally on the Eigenvalue Parameter

Discrete canonical system and non‐Abelian Toda lattice: Bäcklund–Darboux transformation, Weyl functions, and explicit solutions

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