Basis properties of the eigenfunctions of two-interval Sturm–Liouville problems
In this paper a Sturm–Liouville equation together with eigenparameter-dependent boundary-transmission conditions are considered on two disjoint intervals. We construct the resolvent operator and Green’s function and obtain asymptotic approximate formulas for eigenvalues and corresponding eigenfuncti...
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| Veröffentlicht in: | Analysis and mathematical physics 2019-09, Vol.9 (3), p.1363-1382 |
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| container_title | Analysis and mathematical physics |
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| creator | Mukhtarov, O. Sh Aydemir, K. |
| description | In this paper a Sturm–Liouville equation together with eigenparameter-dependent boundary-transmission conditions are considered on two disjoint intervals. We construct the resolvent operator and Green’s function and obtain asymptotic approximate formulas for eigenvalues and corresponding eigenfunctions. The obtained results are implemented to the investigation of the basis properties of the system of eigenfunctions in the Lebesgue space
L
2
with new measures. In particular, we show that the eigenfunction expansion series regarding the convergence behaves in the same way as an ordinary Fourier series. |
| doi_str_mv | 10.1007/s13324-018-0242-8 |
| format | Article |
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L
2
with new measures. In particular, we show that the eigenfunction expansion series regarding the convergence behaves in the same way as an ordinary Fourier series.</description><identifier>ISSN: 1664-2368</identifier><identifier>EISSN: 1664-235X</identifier><identifier>DOI: 10.1007/s13324-018-0242-8</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Eigenvalues ; Eigenvectors ; Fourier series ; Liouville equations ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Operators (mathematics)</subject><ispartof>Analysis and mathematical physics, 2019-09, Vol.9 (3), p.1363-1382</ispartof><rights>Springer Nature Switzerland AG 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-df2462317f6470b7009c7fec811eb4d8308268c9c74cab0a744ae2e531c717ed3</citedby><cites>FETCH-LOGICAL-c316t-df2462317f6470b7009c7fec811eb4d8308268c9c74cab0a744ae2e531c717ed3</cites><orcidid>0000-0001-7480-6857</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13324-018-0242-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13324-018-0242-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Mukhtarov, O. Sh</creatorcontrib><creatorcontrib>Aydemir, K.</creatorcontrib><title>Basis properties of the eigenfunctions of two-interval Sturm–Liouville problems</title><title>Analysis and mathematical physics</title><addtitle>Anal.Math.Phys</addtitle><description>In this paper a Sturm–Liouville equation together with eigenparameter-dependent boundary-transmission conditions are considered on two disjoint intervals. We construct the resolvent operator and Green’s function and obtain asymptotic approximate formulas for eigenvalues and corresponding eigenfunctions. The obtained results are implemented to the investigation of the basis properties of the system of eigenfunctions in the Lebesgue space
L
2
with new measures. In particular, we show that the eigenfunction expansion series regarding the convergence behaves in the same way as an ordinary Fourier series.</description><subject>Analysis</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Fourier series</subject><subject>Liouville equations</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><issn>1664-2368</issn><issn>1664-235X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kMtKAzEUhoMoWGofwN2A6-jJpUm61OINCiIquAsz6ZmaMp2pSabiznfwDX0SZxjRlatz-Pkv8BFyzOCUAeizyITgkgIzFLjk1OyREVNKUi6mz_u_vzKHZBLjGgCYnCqp9IjcX-TRx2wbmi2G5DFmTZmlF8zQr7Au29ol39SD-tZQXycMu7zKHlIbNl8fnwvftDtfVdhXFBVu4hE5KPMq4uTnjsnT1eXj_IYu7q5v5-cL6gRTiS5LLhUXTJdKaig0wMzpEp1hDAu5NAIMV8Z1onR5AbmWMkeOU8GcZhqXYkxOht5u-LXFmOy6aUPdTVouADg3wGediw0uF5oYA5Z2G_wmD--Wge3h2QGe7eDZHp41XYYPmdh56xWGv-b_Q980-HLs</recordid><startdate>20190901</startdate><enddate>20190901</enddate><creator>Mukhtarov, O. Sh</creator><creator>Aydemir, K.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-7480-6857</orcidid></search><sort><creationdate>20190901</creationdate><title>Basis properties of the eigenfunctions of two-interval Sturm–Liouville problems</title><author>Mukhtarov, O. Sh ; Aydemir, K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-df2462317f6470b7009c7fec811eb4d8308268c9c74cab0a744ae2e531c717ed3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analysis</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Fourier series</topic><topic>Liouville equations</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mukhtarov, O. Sh</creatorcontrib><creatorcontrib>Aydemir, K.</creatorcontrib><collection>CrossRef</collection><jtitle>Analysis and mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mukhtarov, O. Sh</au><au>Aydemir, K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Basis properties of the eigenfunctions of two-interval Sturm–Liouville problems</atitle><jtitle>Analysis and mathematical physics</jtitle><stitle>Anal.Math.Phys</stitle><date>2019-09-01</date><risdate>2019</risdate><volume>9</volume><issue>3</issue><spage>1363</spage><epage>1382</epage><pages>1363-1382</pages><issn>1664-2368</issn><eissn>1664-235X</eissn><abstract>In this paper a Sturm–Liouville equation together with eigenparameter-dependent boundary-transmission conditions are considered on two disjoint intervals. We construct the resolvent operator and Green’s function and obtain asymptotic approximate formulas for eigenvalues and corresponding eigenfunctions. The obtained results are implemented to the investigation of the basis properties of the system of eigenfunctions in the Lebesgue space
L
2
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| subjects | Analysis Eigenvalues Eigenvectors Fourier series Liouville equations Mathematical Methods in Physics Mathematics Mathematics and Statistics Operators (mathematics) |
| title | Basis properties of the eigenfunctions of two-interval Sturm–Liouville problems |
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