ABSTRACT

We consider the differential expression https://www.w3.org/1998/Math/MathML"> L [ y ] = − x − γ x x y ′ ′ ,   x ∈ I = [ c , ∞ ) ,   c > 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332623/d03ac290-bd50-452e-ba31-4edd6e078f1a/content/eqn1_1b.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> acting in the Hilbert space ℒ2 (xγ,I) of functions f satisfying https://www.w3.org/1998/Math/MathML">∫Ixγ|f(x)|2dx<∞https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332623/d03ac290-bd50-452e-ba31-4edd6e078f1a/content/ieq0259.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>. Perturbation expressions of the form https://www.w3.org/1998/Math/MathML"> A [ y ] ≡ x − γ a ( x ) y ,   B [ y ] = x − γ b ( x ) y ′ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332623/d03ac290-bd50-452e-ba31-4edd6e078f1a/content/eqn1_2b.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> will be applied to L. The functions a, b will be real or complex-valued functions which are in ℒloc(I), the functions on I which are locally Lebesgue integrable.