Selfadjoint extensions of a singular multipoint differential operator of first order
In this work, we describe all selfadjoint extensions of the minimal operator generated by linear singular multipoint symmetric differential expression $l=(l_1,l_2,l_3)$, $l_k=ifrac{d}{dt}+A_k$ with selfadjoint operator coefficients $A_k$, $k=1,2,3$ in a Hilbert space. This is done as a direct su...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2013-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/129/abstr.html |
| Summary: | In this work, we describe all selfadjoint extensions of the minimal operator generated by linear singular multipoint symmetric differential expression $l=(l_1,l_2,l_3)$, $l_k=ifrac{d}{dt}+A_k$ with selfadjoint operator coefficients $A_k$, $k=1,2,3$ in a Hilbert space. This is done as a direct sum of Hilbert spaces of vector-functions $$ L_2(H,(-infty ,a_1))oplus L_2(H,(a_2,b_2)) oplus L_2(H,(a_3,+infty)) $$ where $-infty <a_1<a_2<b_2<a_3<+infty$. Also, we study the structure of the spectrum of these extensions. |
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| ISSN: | 1072-6691 |