The generalized Green’s function for an $n$th order linear differential operator
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- by John Locker PDF
- Trans. Amer. Math. Soc. 228 (1977), 243-268 Request permission
Abstract:
The generalized Green’s function $K(t,s)$ for an nth order linear differential operator L is characterized in terms of the 2nth order differential operators $L{L^\ast }$ and ${L^\ast }L$. The development is operator oriented and takes place in the Hilbert space ${L^2}[a,b]$. Two features of the characterization are a determination of the jumps occurring in the derivatives of orders n, $n + 1, \ldots ,2n - 1$ at $t = s$ and a determination of the boundary conditions satisfied by the functions $K(a, \cdot )$ and $K(b,\cdot )$. Several examples are given to illustrate the properties of the generalized Green’s function.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 228 (1977), 243-268
- MSC: Primary 34B05; Secondary 47E05
- DOI: https://doi.org/10.1090/S0002-9947-1977-0481204-0
- MathSciNet review: 0481204