Geodesic
On~equiconvergence of expansions in trigonometric Fourier series and in principal functions of ordinary differential operators
Izvestiya. Mathematics , Tome 24 (1985) no. 3, pp. 567-582.

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A regularity concept is given for ordinary differential pencils of a general form in a space of vector-valued functions, and this concept is subjected to analysis. Theorems are established asserting that the Fourier series of an arbitrary vector-valued function in the system of eigenelements of the pencils is equiconvergent with the usual trigonometric Fourier series of the components of this vector-valued function. Bibliography: 7 titles. 
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A. I. Vahabov. On~equiconvergence of expansions in trigonometric Fourier series and in principal functions of ordinary differential operators. Izvestiya. Mathematics , Tome 24 (1985) no. 3, pp. 567-582. http://geodesic.mathdoc.fr/item/IM2_1985_24_3_a6/

[1] Birkhoff G. D., “Boundary value and expansion problem of ordinary linear differential equations”, Trans. Amer. Math. Soc., 9 (1908), 373–395 | DOI | MR | Zbl

[2] Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh differentsialnykh uravnenii i razlozhenii proizvolnykh funktsii v ryady, Petrograd, 1917 | Zbl

[3] Tamarkin Ya. D., “Some general problems of theory of ordinary linear differential equations and expansion of an arbitrary function in series of fundamental functions”, Math. Z., 27 (1927), 1–54 | DOI | MR | Zbl

[4] Ilin V. A., “O ravnoskhodimosti razlozhenii v trigonometricheskii ryad Fure i po sobstvennym funktsiyam puchka M. V. Keldysha obyknovennykh nesamosopryazhennykh differentsialnykh operatorov”, Dokl. AN SSSR, 225:3 (1975), 497–494 ; “О свойствах приведенной подсистемы собственных и присоединенных функций пучка М. В. Келдыша обыкновенных дифференциальных операторов”, Докл. АН СССР, 230:1 (1976), 30–33 ; “Необходимые и достаточные условия базисности и равносходимости с тригонометрическим рядом спектральных разложений, I, II”, Дифференциальные уравнения, 5 (1980), 771–794 ; 6 (1980), 981–1109 | MR | MR

[5] Khromov A. P., “Teoremy ravnoskhodimosti dlya integro-differentsialnykh i integralnykh operatorov”, Matem. sb., 114(156):3 (1981), 378–405 | MR | Zbl

[6] Vagabov A. I., “O ravnoskhodimosti razlozhenii v trigonometricheskii ryad Fure i po glavnym funktsiyam obyknovennykh differentsialnykh operatorov”, Dokl. AN SSSR, 254:6 (1981), 1294–1297 | MR

[7] Keldysh M. V., “O sobstvennykh funktsiyakh i sobstvennykh znacheniyakh nekotorykh klassov nesamosopryazhennykh uravnenii”, Dokl. AN SSSR, 77:1 (1951), 11–14 | Zbl