A Prüfer transformation for nonselfadjoint systems
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- by Kurt Kreith
- Proc. Amer. Math. Soc. 31 (1972), 147-151
- DOI: https://doi.org/10.1090/S0002-9939-1972-0293216-1
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Abstract:
The Prüfer transformation has been generalized to selfadjoint matrix differential equations by J. Barrett and others. Those results are extended to nonselfadjoint abstract systems of the form considered by Kamke in the scalar case and Reid in the matrix case.References
- Heinz Prüfer, Neue Herleitung der Sturm-Liouvilleschen Reihenentwicklung stetiger Funktionen, Math. Ann. 95 (1926), no. 1, 499–518 (German). MR 1512291, DOI 10.1007/BF01206624
- John H. Barrett, A Prüfer transformation for matrix differential equations, Proc. Amer. Math. Soc. 8 (1957), 510–518. MR 87821, DOI 10.1090/S0002-9939-1957-0087821-7
- Garret J. Etgen, Oscillatory properties of certain nonlinear matrix differential systems of second order, Trans. Amer. Math. Soc. 122 (1966), 289–310. MR 190421, DOI 10.1090/S0002-9947-1966-0190421-1
- Garret J. Etgen, A note on trigonometric matrices, Proc. Amer. Math. Soc. 17 (1966), 1226–1232. MR 213646, DOI 10.1090/S0002-9939-1966-0213646-0
- William T. Reid, A Prüfer transformation for differential systems, Pacific J. Math. 8 (1958), 575–584. MR 99474
- William T. Reid, Generalized polar coordinate transformations for differential systems, Rocky Mountain J. Math. 1 (1971), no. 2, 383–406. MR 280769, DOI 10.1216/RMJ-1971-1-2-383
- Einar Hille, Lectures on ordinary differential equations, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0249698
- Donald C. Benson and Kurt Kreith, On abstract Pruefer transformations, Proc. Amer. Math. Soc. 26 (1970), 137–140. MR 262638, DOI 10.1090/S0002-9939-1970-0262638-5
- E. Kamke, A new proof of Sturm’s comparison theorems, Amer. Math. Monthly 46 (1939), 417–421. MR 326, DOI 10.2307/2303035
- E. Kamke, Über Sturms Vergleichssätze für homogene lineare Differentialgleichungen zweiter Ordnung und Systeme von zwei Differentialgeichungen erster Ordnung, Math. Z. 47 (1942), 788–795 (German). MR 14524, DOI 10.1007/BF01180986
- John H. Barrett, Second order complex differential equations with a real independent variable, Pacific J. Math. 8 (1958), 187–200. MR 98213
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 147-151
- MSC: Primary 34G05; Secondary 46N05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0293216-1
- MathSciNet review: 0293216