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Ein Äquikonvergenzsatz für eine Klasse von singulären Differentialoperatoren. (German) Zbl 0339.34020

MSC:

34L99 Ordinary differential operators
34B05 Linear boundary value problems for ordinary differential equations
47E05 General theory of ordinary differential operators
47A25 Spectral sets of linear operators
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
44A05 General integral transforms
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References:

[1] Benzinger, H.E.: Equiconvergence for singular differential operators. J. math. Analysis Appl.32, 338-351 (1970) · Zbl 0208.11103
[2] Brauer, F.: Spectral theory for linear systems of differential equations. Pacific J. Math.10, 17-34 (1960) · Zbl 0188.46302
[3] Eberhard, W., Freiling, G.: Das Verhalten der Greenschen Matrix und der Entwicklungen nach EigenfunktionenN-regulärer Eigenwertprobleme. Math. Z.136, 13-30 (1974) · Zbl 0265.34033
[4] Freiling, G.: Nichtselbstadjungierte Differentialoperatoren im nichtkompakten Fall. Math. Z.149, 267-279 (1976) · Zbl 0323.34018
[5] Funtakov, V.: Expansions in Eigenfunctions of a non-selfadjoint differential operator of arbitrary even order in the semi-axis [0,?). Izvestija Akad. Nauk Azerbaîd?. SSR, Ser. fiz-tehn. mat. Nauk1960, 3-19 und1961, 3-21
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[7] Kodaira, K.: On ordinary differential equations of any even order and the corresponding eigenfunction expansions. Amer. J. Math.72, 502-544 (1950) · Zbl 0054.03903
[8] Ljance, V.E.: A differential operator with spectral singularities. Amer. math. Soc., Translat., II. Ser.60, 185-283 (1967)
[9] Neumark, M.A.: Investigation of the spectrum and the expansion in eigenfunctions of a nonselfadjoint differential operator of the second order on a semi axis. Trudy Moskov. mat. Ob??.3, 181-270 (1954)
[10] Niessen, H.D., Schneider, A.: Integraltransformationen zu singulären S-hermiteschen Rand-Eigenwertproblemen. Manuscripta math.5, 133-145 (1971) · Zbl 0221.34014
[11] Pavlov, B.S.: On the spectral theory of non-self-adjoint differential operators. Doklady Akad. Nauk. SSSR146, 1267-1270 (1962)
[12] Plejel, A.: Spectral theory for pairs of ordinary formally self-adjoint differential operators. J. Indian math. Soc. n. Ser.34, 259-268 (1970)
[13] Stone, M.H.: A comparison of the series of Fourier and Birkhoff. Trans. Amer. math. Soc.28, 695-761 (1926) · JFM 52.0456.02
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