The generalized Green's function for an th order linear differential operator

Author:
John Locker

Journal:
Trans. Amer. Math. Soc. **228** (1977), 243-268

MSC:
Primary 34B05; Secondary 47E05

MathSciNet review:
0481204

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Abstract: The generalized Green's function for an *n*th order linear differential operator *L* is characterized in terms of the 2*n*th order differential operators and . The development is operator oriented and takes place in the Hilbert space . Two features of the characterization are a determination of the jumps occurring in the derivatives of orders *n*, at and a determination of the boundary conditions satisfied by the functions and . Several examples are given to illustrate the properties of the generalized Green's function.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1977-0481204-0

Keywords:
Generalized Green's function,
differential operator,
jump conditions,
boundary conditions,
generalized inverse,
quasi-derivatives,
Green's formula

Article copyright:
© Copyright 1977
American Mathematical Society