Interpolation of nonlinear functionals by integral continued fractions

Mykhal’chuk, B. R.

doi:10.1007/bf02592477

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Cited by 4 publications

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“…[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].…”

Section: Introductionmentioning

confidence: 99%

Interpolation of functionals by integral continued C-fractions

Макаров¹,

Pahirya²

2018

Dopov. Nac. akad. nauk Ukr.

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Section: Introductionmentioning

confidence: 99%

Interpolation of functionals by integral continued C-fractions

Макаров¹,

Pahirya²

2018

Dopov. Nac. akad. nauk Ukr.

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Interpolational Integral Continued Fractions

Макаров

Khlobystov

Mykhal’chuk

2003

Ukrainian Mathematical Journal

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

Kutsenko

2017

Journal of Mathematical Physics

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We show that spectral problems for periodic operators on lattices with embedded defects of lower dimensions can be solved with the help of matrix-valued integral continued fractions. While these continued fractions are usual in the approximation theory, they are less known in the context of spectral problems. We show that the spectral points can be expressed as zeroes of determinants of the continued fractions. They are also useful in the study of inverse problems (one-to-one correspondence between spectral data and defects). Finally, the explicit formula for the resolvent in terms of the continued fractions is also provided. We apply some of our results to the Schrödinger operator acting on the graphene with line and point defects.

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Interpolation of nonlinear functionals by integral continued fractions

Cited by 4 publications

References 3 publications

Interpolation of functionals by integral continued C-fractions

Interpolation of functionals by integral continued C-fractions

Interpolational Integral Continued Fractions

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

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