## On the polar equations for linear systems and related nonlinear matrix differential equations

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- by Glen J. Culler PDF
- Trans. Amer. Math. Soc.
**118**(1965), 390-405 Request permission

## References

- George D. Birkhoff,
*On the asymptotic character of the solutions of certain linear differential equations containing a parameter*, Trans. Amer. Math. Soc.**9**(1908), no. 2, 219–231. MR**1500810**, DOI 10.1090/S0002-9947-1908-1500810-1
—, - Earl A. Coddington and Norman Levinson,
*Theory of ordinary differential equations*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR**0069338** - Erhard Heinz,
*Beiträge zur Störungstheorie der Spektralzerlegung*, Math. Ann.**123**(1951), 415–438 (German). MR**44747**, DOI 10.1007/BF02054965 - Magnus R. Hestenes,
*Applications of the theory of quadratic forms in Hilbert space to the calculus of variations*, Pacific J. Math.**1**(1951), 525–581. MR**46590** - G. D. Birkhoff and M. R. Hestenes,
*Natural isoperimetric conditions in the calculus of variations*, Duke Math. J.**1**(1935), no. 2, 198–286. MR**1545876**, DOI 10.1215/S0012-7094-35-00118-1 - Magnus R. Hestenes,
*Inversion of matrices by biorthogonalization and related results*, J. Soc. Indust. Appl. Math.**6**(1958), 51–90. MR**92215**
—, - Magnus R. Hestenes,
*Sufficient conditions for the problem of Bolza in the calculus of variations*, Trans. Amer. Math. Soc.**36**(1934), no. 4, 793–818. MR**1501767**, DOI 10.1090/S0002-9947-1934-1501767-5
J. von Neumann, - J. von Neumann,
*Über adjungierte Funktionaloperatoren*, Ann. of Math. (2)**33**(1932), no. 2, 294–310 (German). MR**1503053**, DOI 10.2307/1968331
—, - A. Ostrowski,
*Bounds for the greatest latent root of a positive matrix*, J. London Math. Soc.**27**(1952), 253–256. MR**49152**, DOI 10.1112/jlms/s1-27.2.253 - A. M. Ostrowski and Olga Taussky,
*On the variation of the determinant of a positive definite matrix*, Nederl. Akad. Wetensch. Proc. Ser. A. 54 = Indagationes Math.**13**(1951), 383–385. MR**0047597** - A. M. Ostrowski,
*On the spectrum of a one-parametric family of matrices*, J. Reine Angew. Math.**193**(1954), 143–160. MR**66336**, DOI 10.1515/crll.1954.193.143 - Alexander Ostrowski,
*Über Normen von Matrizen*, Math. Z.**63**(1955), 2–18 (German). MR**72100**, DOI 10.1007/BF01187920 - William T. Reid,
*Oscillation criteria for linear differential systems with complex coefficients*, Pacific J. Math.**6**(1956), 733–751. MR**84655** - William T. Reid,
*A comparison theorem for self-adjoint differential equations of second order*, Ann. of Math. (2)**65**(1957), 197–202. MR**92045**, DOI 10.2307/1969673 - William T. Reid,
*Adjoint linear differential operators*, Trans. Amer. Math. Soc.**85**(1957), 446–461. MR**88625**, DOI 10.1090/S0002-9947-1957-0088625-6 - William T. Reid,
*Remarks on a matrix transformation for linear differential equations*, Proc. Amer. Math. Soc.**8**(1957), 708–712. MR**86962**, DOI 10.1090/S0002-9939-1957-0086962-8 - William T. Reid,
*Principal solutions of non-oscillatory self-adjoint linear differential systems*, Pacific J. Math.**8**(1958), 147–169. MR**98220** - William T. Reid,
*A Prüfer transformation for differential systems*, Pacific J. Math.**8**(1958), 575–584. MR**99474** - Frigyes Riesz and Béla Sz.-Nagy,
*Functional analysis*, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR**0071727** - Marvin Rosenblum,
*On the operator equation $BX-XA=Q$*, Duke Math. J.**23**(1956), 263–269. MR**79235** - Angus E. Taylor,
*Conjugations of complex linear spaces*, Univ. California Publ. Math. (N.S.)**2**(1944), 85–102 [No. 1, Seminar Rep. in Math. (Los Angeles)]. MR**10256** - Angus E. Taylor,
*Analytic functions in general analysis*, Ann. Scuola Norm. Super. Pisa Cl. Sci. (2)**6**(1937), no. 3-4, 277–292. MR**1556793**

*On matrices of analytic functions*, Math. Ann.

**74**(1913), 122.

*On a representation of general operators*. (Unpublished).

*Allgemeine Eigenwerttheorie Hermitescher Functionaloperatoren*, Math. Ann.

**102**(1929), 49.

*Some matrix-inequalities and metrization of matric-space*, Forsch.-Inst. Math. Mech. Univ. Tomsk

**1**(1937), 286-299.

## Additional Information

- © Copyright 1965 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**118**(1965), 390-405 - MSC: Primary 34.20
- DOI: https://doi.org/10.1090/S0002-9947-1965-0178194-9
- MathSciNet review: 0178194