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1: 18.1 Notation

… ►or the dilated Chebyshev polynomials of the first and second kinds: ►

$C_n\left(x\right)=2T_n\left(\frac{1}{2}x\right),$

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$S_n\left(x\right)=U_n\left(\frac{1}{2}x\right).$

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2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►This dilatation transformation, which does require analyticity of $q(x)$ in (1.18.28), or an analytic approximation thereto, leaves the poles, corresponding to the discrete spectrum, invariant, as they are, as is the branch point, actual singularities of $⟨{\left(z-T\right)}^{-1}f,f⟩$. …

3: Bibliography S

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Resonances in $n$-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Ann. of Math. (2) 97, pp. 247–274.

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External Links:

ISSN 0003-486X, Document, Link, MathReview (K. Kumar)

Referenced by:

§1.18(viii).

Encodings:

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