On abstract Pruefer transformations
Authors:
Donald C. Benson and Kurt Kreith
Journal:
Proc. Amer. Math. Soc. 26 (1970), 137-140
MSC:
Primary 34.95
DOI:
https://doi.org/10.1090/S0002-9939-1970-0262638-5
MathSciNet review:
0262638
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Abstract | References | Similar Articles | Additional Information
Abstract: The Pruefer transformation has been generalized to matrix differential equations by John Barrett, and Barrett’s results have been partly extended to the case of functions which take values in a ${B^ \ast }$-algebra by Einar Hille. By modifying Barrett’s proof, generalizations in the ${B^ \ast }$-algebra case become possible.
- John H. Barrett, A Prüfer transformation for matrix differential equations, Proc. Amer. Math. Soc. 8 (1957), 510–518. MR 87821, DOI https://doi.org/10.1090/S0002-9939-1957-0087821-7
- William T. Reid, A Prüfer transformation for differential systems, Pacific J. Math. 8 (1958), 575–584. MR 99474
- 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 https://doi.org/10.1090/S0002-9947-1966-0190421-1
- Einar Hille, Lectures on ordinary differential equations, Addison-Wesley Publ. Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0249698
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
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Additional Information
Keywords:
Pruefer transformation,
<!– MATH ${B^ \ast }$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${B^ \ast }$">-algebra,
generalized sines and cosines,
Picard existence theorem
Article copyright:
© Copyright 1970
American Mathematical Society