A canonical form for a class of ordinary differential operators

Benzinger, Harold E.

doi:10.1090/S0002-9939-1977-0445053-7

A canonical form for a class of ordinary differential operators
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by Harold E. Benzinger PDF

Proc. Amer. Math. Soc. 63 (1977), 281-286 Request permission

Abstract:

A canonical form is developed for each member of a large class of nth order linear ordinary differential operators, acting on ${L^p}(0,1)$. This canonical form shows how the Fourier-like behavior of eigenfunction expansions is related to structural properties of the operators.

References

Harold E. Benzinger, Green’s function for ordinary differential operators, J. Differential Equations 7 (1970), 478–496. MR 262583, DOI 10.1016/0022-0396(70)90096-3
Harold E. Benzinger, The $L^{p}$ behavior of eigenfunction expansions, Trans. Amer. Math. Soc. 174 (1972), 333–344 (1973). MR 328189, DOI 10.1090/S0002-9947-1972-0328189-0
Harold E. Benzinger, Pointwise and norm convergence of a class of biorthogonal expansions, Trans. Amer. Math. Soc. 231 (1977), no. 1, 259–271. MR 442588, DOI 10.1090/S0002-9947-1977-0442588-2
George D. Birkhoff, Boundary value and expansion problems of ordinary linear differential equations, Trans. Amer. Math. Soc. 9 (1908), no. 4, 373–395. MR 1500818, DOI 10.1090/S0002-9947-1908-1500818-6
I. I. Hirschman Jr., On multiplier transformations, Duke Math. J. 26 (1959), 221–242. MR 104973
Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482

Linear differential operators

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M. H. Stone, A comparison of the series of Fourier and Birkhoff, Trans. Amer. Math. Soc. 28 (1926), no. 4, 695–761. MR 1501372, DOI 10.1090/S0002-9947-1926-1501372-6