1D nonnegative Schrodinger operators with point interactions
Let $Y$ be an infinite discrete set of points in $dR$,satisfying the condition $inf{|y-y'|,; y,y'in Y, y'ey}>0.$ In the paper we prove that the systems${delta(x-y)}_{yin Y}, ;{delta'(x-y)}_{yin Y},{delta(x-y),;delta'(x-y)}_{yin Y}$ {form Riesz} bases in the corresponding...
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Ivan Franko National University of Lviv
2013-07-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/texts/2013/39_2/150-163.pdf |
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| author | Yu. G. Kovalev |
| author_facet | Yu. G. Kovalev |
| author_sort | Yu. G. Kovalev |
| collection | DOAJ |
| description | Let $Y$ be an infinite discrete set of points in $dR$,satisfying the condition $inf{|y-y'|,; y,y'in Y, y'ey}>0.$ In the paper we prove that the systems${delta(x-y)}_{yin Y}, ;{delta'(x-y)}_{yin Y},{delta(x-y),;delta'(x-y)}_{yin Y}$ {form Riesz} bases in the corresponding closed linear spans in the Sobolev spaces $W_2^{-1}(dR)$ and $W_2^{-2}(dR)$. As an application, we prove the transversalness of the Friedrichs and Kreui n nonnegative selfadjoint extensions of the nonnegative symmetric operators $A_0$, $A'$, and $H_0$ defined {as restrictions} of the operator $A =-frac{ d^2}{ dx^2},$ $dom (A)=W^2_2(dR)${to} the linear manifolds $dom (A_0)=left{ finW_2^2(mathbb{R})colon f(y)=0,; yin Y ight}$, $dom(A')={ gin W_2^2(mathbb{R})colon g'(y)=0,; yin Y },$ and$dom (H_0)=left{fin W_2^2(mathbb{R})colonf(y)=0,;f'(y)=0,; yin Y ight}$, respectively. Using thedivergence forms, the basic nonnegative boundary triplets for$A^*_0$, $A'^*$, and $H^*_0$ are constructed. |
| format | Article |
| id | doaj-art-e6585dc4cb90434ca169d400ceab50d4 |
| institution | Kabale University |
| issn | 1027-4634 |
| language | deu |
| publishDate | 2013-07-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-e6585dc4cb90434ca169d400ceab50d42025-08-20T03:57:59ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342013-07-013921501631D nonnegative Schrodinger operators with point interactionsYu. G. KovalevLet $Y$ be an infinite discrete set of points in $dR$,satisfying the condition $inf{|y-y'|,; y,y'in Y, y'ey}>0.$ In the paper we prove that the systems${delta(x-y)}_{yin Y}, ;{delta'(x-y)}_{yin Y},{delta(x-y),;delta'(x-y)}_{yin Y}$ {form Riesz} bases in the corresponding closed linear spans in the Sobolev spaces $W_2^{-1}(dR)$ and $W_2^{-2}(dR)$. As an application, we prove the transversalness of the Friedrichs and Kreui n nonnegative selfadjoint extensions of the nonnegative symmetric operators $A_0$, $A'$, and $H_0$ defined {as restrictions} of the operator $A =-frac{ d^2}{ dx^2},$ $dom (A)=W^2_2(dR)${to} the linear manifolds $dom (A_0)=left{ finW_2^2(mathbb{R})colon f(y)=0,; yin Y ight}$, $dom(A')={ gin W_2^2(mathbb{R})colon g'(y)=0,; yin Y },$ and$dom (H_0)=left{fin W_2^2(mathbb{R})colonf(y)=0,;f'(y)=0,; yin Y ight}$, respectively. Using thedivergence forms, the basic nonnegative boundary triplets for$A^*_0$, $A'^*$, and $H^*_0$ are constructed.http://matstud.org.ua/texts/2013/39_2/150-163.pdfpoint interactionRiesz basisboundary tripletthe Friedrichs extensionthe Krein extension |
| spellingShingle | Yu. G. Kovalev 1D nonnegative Schrodinger operators with point interactions Математичні Студії point interaction Riesz basis boundary triplet the Friedrichs extension the Krein extension |
| title | 1D nonnegative Schrodinger operators with point interactions |
| title_full | 1D nonnegative Schrodinger operators with point interactions |
| title_fullStr | 1D nonnegative Schrodinger operators with point interactions |
| title_full_unstemmed | 1D nonnegative Schrodinger operators with point interactions |
| title_short | 1D nonnegative Schrodinger operators with point interactions |
| title_sort | 1d nonnegative schrodinger operators with point interactions |
| topic | point interaction Riesz basis boundary triplet the Friedrichs extension the Krein extension |
| url | http://matstud.org.ua/texts/2013/39_2/150-163.pdf |
| work_keys_str_mv | AT yugkovalev 1dnonnegativeschrodingeroperatorswithpointinteractions |