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On the limit-classifications of even and odd-order formally symmetric differential expressions | | K V Alice
; V Krishna Kumar
; A Padmanabhan
; | | Date: |
8 Mar 2004 | | Journal: | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 1, February 2004, pp. 65-78 | | Subject: | Classical Analysis and ODEs | math.CA | | Abstract: | In this paper we consider the formally symmetric differential expression $M[cdot]$ of any order (odd or even) $geq 2$. We characterise the dimension of the quotient space $D(T_{max})/D(T_{min})$ associated with $M[cdot]$ in terms of the behaviour of the determinants {equation*} detlimits_{r,sin {f N}_{n}} [[f_{r}g_{s}](infty)] {equation*} where $1leq nleq$ (order of the expression + 1); here $[fg](infty) = limlimits_{x oinfty}[fg](x)$, where $[fg](x)$ is the sesquilinear form in $f$ and $g$ associated with $M$. These results generalise the well-known theorem that $M$ is in the limit-point case at $infty$ if and only if $[fg](infty) = 0$ for every $f,gin$ the maximal domain $Delta$ associated with $M$. | | Source: | arXiv, math.CA/0403128 | | Services: | Forum | Review | PDF | Favorites | |
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