Interpolational Integral Continued Fractions

Interpolation integral continued fraction with twofold node

“…Sufficient conditions of integral fraction interpolativity (see [1]) were discovered in the work [2]. These conditions state that the substitution rule takes place.…”

“…The ICF investigated in [1,2] has the following problem. In (1) we put x i (z) ≡ x i = const, i = 0, .…”

Interpolation of functionals by integral continued C-fractions

“…[5]. The problem of interpolation with integral continued fractions was first considered in the article [6], further expansions and generalizations of this work are contained in the paper [7].…”

Application of matrix-valued integral continued fractions to spectral problems on periodic graphs with defects

“…Suppose that we want to construct the operator A (5)-(6) with the spectrum σ = ∪σ j , where σ 0 = [0, 1], σ 1 = [0.5, 1.5], and σ 2 = 2. In order to do this we can choose any real continuous functions λ j satisfying (20) with λ j ([0, 1] N −j ) = σ j , and use after the procedure from Theorem 1.4.ii) along with Definition 1.1. Ok, suppose that we want λ 0 = k 1 k 2 , λ 1 = 0.5 + k 2 , and λ 2 = 2.…”

“…Classical integral CF are introduced in [17], [18] as solutions of differential equations. They are also discussed in the context of interpolation theory, see, e.g., [19], [20]. At the same time, probably there are no papers devoted to integral CF or MCF of the form (8).…”