The Basis Property of the System of Weak Eigenfunctions of a Discontinuous Sturm–Liouville Problem

Olğar, Hayati; Muhtarov, Fahreddin

doi:10.1007/s00009-017-0915-9

Cited by 14 publications

(2 citation statements)

References 18 publications

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“…Boundary value problems including transmission conditions appears in many fields of natural sciences. Recently, such type of transmission problems have been an important topic in theoretical and applied mathematics (see, [17][18][19][20][21][22][23][24][25][26][27][28]). In this study we will investigate some basic spectral properties of a new type periodic Sturm-Liouville problems.…”

Section: Introductionmentioning

confidence: 99%

The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions

Aydemir

Mukhtarov

2021

Journal of New Theory

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In this paper, we study the periodic Sturm-Liouville problem, defined on three non-intersecting intervals with four supplementary conditions which are imposed at two internal points of interaction, the so-called transmission conditions. We first prove that the eigenvalues are real and the system of eigenfunctions is an orthogonal system. Secondly, some auxiliary initial-value problems are defined and transmittal-characteristic function is constructed in terms of solutions of these initial-value problems. Finally, we establish that the eigenvalues of the considered problem are the zeros of the transmittal-characteristic function.

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Section: Introductionmentioning

confidence: 99%

The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions

Aydemir

Mukhtarov

2021

Journal of New Theory

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“…Since then many results on the Riesz basis have been obtained [3][4][5]. Also the Riesz basis of the systems of sines and cosines in 2 [0, ] and Riesz basis associated with Sturm-Liouville problems have been studied in many papers [6][7][8][9][10][11][12]; moreover, on the problems of expansion of eigenfunctions, we refer to [13][14][15][16][17][18] and references cited therein.…”

Section: Introductionmentioning

confidence: 99%