Elliptic Problems Involving an Indefinite Weight Function

1996 ◽  
pp. 105-124 ◽  
Author(s):  
M. Faierman ◽  
H. Langer
Keyword(s):  
Weight Function ◽  
Elliptic Problems ◽  
Indefinite Weight ◽  
Indefinite Weight Function

Sturm-Liouville operators with an indefinite weight function

1977 ◽  
Vol 78 (1-2) ◽  
pp. 161-191 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Weight Function ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Scalar Product ◽  
Main Tool ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Sturm Liouville ◽  
Liouville Operators

SynopsisSpectral properties of the singular Sturm-Liouville equation –(p−1y′)′ + qy = λry with an indefinite weight function r are studied in . The main tool is the theory of definitisable operators in spaces with an indefinite scalar product.

Some remarks on a paper by W. N. Everitt

1977 ◽  
Vol 78 (1-2) ◽  
pp. 71-79 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Hilbert Space ◽  
Weight Function ◽  
Selfadjoint Operator ◽  
Krein Space ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Kreĭn Space ◽  
Pontrjagin Space

Everitt has shown [1[, that for α ∊ [0, π/2] the undernoted problem (1.1–2) with an indefinite weight function r can be represented by a selfadjoint operator in a suitable Hilbert space. This result is extended to arbitrary α ∊ [0, π), replacing the Hilbert space in some cases by a Pontrjagin space with index one. The problem is also treated in the Krein space generated by the weight function r.

L∞ bounds of eigenfunctions with an indefinite weight function

2021 ◽  
Vol 117 ◽  
pp. 107095
Author(s):  
Jian-Wen Sun ◽  
Yan-Hua Xing
Keyword(s):  
Weight Function ◽  
Indefinite Weight ◽  
Indefinite Weight Function

A Titchmarsh-Weyl matrix function for symmetric differential equations of order 2n with an indefinite weight function

1984 ◽  
Vol 98 (3-4) ◽  
pp. 311-337
Author(s):  
Karim Daho
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Weight Function ◽  
Matrix Function ◽  
Present Author ◽  
Krein Space ◽  
Indefinite Weight ◽  
Weyl Matrix ◽  
Indefinite Weight Function ◽  
Image Position

SynopsisA Titchmarsh-Weyl matrix function W(λ) is defined for the differential equation of order 2nwith po>0, pk≧0, k = 1, 2, …, n on 005B;0, b), λєℂ and an indefinite weight function r. It is shown that this function W(λ) belongs to some class and that some operators associated with the above equation are definitizable in the Krein space . In the particular case n = 1, these results are contained in an earlier paper by the present author and H. Langer.

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