We consider a regular singular Sturm -Liouville operator on the line segment [0,1]. We impose certain boundary conditions such that we obtain a semibounded self-adjoint operator. It is known (cf. Theorem 1.1 below) that the (-function of this operator ha8 a meromorphic continuation to the whole comp
Bounded solutions and absolute continuity of Sturm-Liouville operators
✍ Scribed by Günter Stolz
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 949 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0022-247X
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## Abstract For __α__ ∈ [0, 2__π__], consider the Sturm‐Liouville equation on the half line __y__″(__x__) + (__λ__ − __q__(__x__))__y__(__x__) = 0, 0 ≤ __x__ < ∞, with __y__(0) = sin__α__, __y__′(0) = −cos__α__. For each __λ__ > 0, denote by __ϕ__(__x, λ__) the solution of the above initial‐v
Consider the STURM -LIOUVIUE differential expression &U P€C', qEC, p ( z ) =-0, q(z) &Po=--0 0 1 2-€[0, -1 I Ay=aS1p, y~ED(A)=C,(O, =) . -( p ( ~) 21')' + ~( 2 ) U , 0 sz -= m , with and define the (minimal) operator A , A considered a8 an operator in the HILBERT space H = L?( 0, a) is bounded from