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Let B be the elementary cell of : d ti bi : 0 ≤ ti < 1 . 18) i=1 Every point x ∈ Rd is uniquely representable in the form x = p + γ , where p ∈ B, γ ∈ . 20) where fˆ(s) is the inverse Fourier transform of a function f ∈ L2 (Rd ): fˆ(s) = 1 (2π )d/2 f (x)eisx dx . 21) Rd The operator U decomposes both H 0 and HT into direct integrals. Namely, let H 0 = U H 0 U −1 , HT = U HT U −1 , then ⊕ H0 = B ⊕ H 0 (p)dp , HT = B HT (p)dp. 22) 34 S. Albeverio, V. A. 23) where the domain D = D(H 0 (p)) is independent of p: D = {ϕ ∈ l 2 ( ) : γ 2 ϕ(γ ) γ∈ ∈ l 2 ( )}.

Math. Phys. : Spectrum and eigenfunctions of Schrödinger operator with zero-range potential of the homogenous lattice type in three dimensional space. (Russian). Teor. i. Mat. Fiz. 57, 304–313 (1983); Engl. : Theor. and Math. Phys. : Perturbation theory for the Schrödinger operator with a periodic potential. Lect. Notes Maths. : Point interactions in two dimensions: Basic properties, approximations and applications to solid state physics. J. reine u. angew. Math. 380, 87–107 (1987) 48 S. Albeverio, V.

7. Elliptic Analogues of Hypergeometric Functions . . . . . . . . 8. Finite-Dimensional Biorthogonality . . . . . . . . . . . 9. Duality Property and the Normalization Constants . . . . . . . 10. Möbius Transformations of the Grids and Some Other Similarity Reductions 11. General Elliptic Biorthogonal Rational Functions . . . . . . . 12. Conclusions . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . .

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