{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,31]],"date-time":"2023-01-31T08:34:14Z","timestamp":1675154054214},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"1","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[1998,3]]},"abstract":"\n The software package SLEDGE has as one of its options the estimation of spectral density functions\n p(t)<\/jats:italic>\n for a wide class of singular Strurm-Liouville problems. In this article the underlaying theory and implementation issues are discussed. Several examples exhibiting quite varied asymptotic behavior in\n p<\/jats:italic>\n are presented.\n <\/jats:p>","DOI":"10.1145\/285861.285867","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:29:03Z","timestamp":1027769343000},"page":"107-129","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra"],"prefix":"10.1145","volume":"24","author":[{"given":"C. T.","family":"Fulton","sequence":"first","affiliation":[{"name":"Florida Institute of Technology, Melbourne"}]},{"given":"S.","family":"Pruess","sequence":"additional","affiliation":[{"name":"Colorado School of Mines, Golden"}]}],"member":"320","published-online":{"date-parts":[[1998,3]]},"reference":[{"key":"e_1_2_1_1_1","series-title":"Lecture Notes in Mathematics","volume-title":"Ordinary and Partial Differential Equations, Proceedings of the 7th Conference (Dundee, Mar. 29-Apr. 2)","author":"ATKINSON F.","unstructured":"ATKINSON , F. 1982. On the asymptotic behaviour of the Titchmarsh-Weyl m-coefficient and the spectral function for scalar second-order differential expressions . In Ordinary and Partial Differential Equations, Proceedings of the 7th Conference (Dundee, Mar. 29-Apr. 2) . Lecture Notes in Mathematics , vol. 964 . Springer-Verlag , New York, NY , 1-27. ATKINSON, F. 1982. On the asymptotic behaviour of the Titchmarsh-Weyl m-coefficient and the spectral function for scalar second-order differential expressions. In Ordinary and Partial Differential Equations, Proceedings of the 7th Conference (Dundee, Mar. 29-Apr. 2). Lecture Notes in Mathematics, vol. 964. Springer-Verlag, New York, NY, 1-27."},{"key":"e_1_2_1_2_1","volume-title":"The relation between asymptotic behaviour and spectral density for Sturm-Liouville operators. Manuscript","author":"ATKINSON F.","unstructured":"ATKINSON , F. 1985. The relation between asymptotic behaviour and spectral density for Sturm-Liouville operators. Manuscript , Argonne National Laboratory , Argonne, IL . ATKINSON, F. 1985. The relation between asymptotic behaviour and spectral density for Sturm-Liouville operators. Manuscript, Argonne National Laboratory, Argonne, IL."},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1017\/S0308210500025968","article-title":"Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit circle singularity","volume":"99","author":"ATKINSON F.","year":"1984","unstructured":"ATKINSON , F. AND FULTON , C. 1984 . Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit circle singularity , I. Proc. Roy. Soc. Edinburgh 99A , 51 - 70 . ATKINSON, F. AND FULTON, C. 1984. Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit circle singularity, I. Proc. Roy. Soc. Edinburgh 99A, 51-70.","journal-title":"I. Proc. Roy. Soc. Edinburgh"},{"key":"e_1_2_1_4_1","volume-title":"Proc. Roy. Soc","author":"ATKINSON F.","year":"1999","unstructured":"ATKINSON , F. AND FULTON , C. 1999 . Asymptotics of the Titchmarsh-Weyl m-coefficient for non-integrable potentials . Proc. Roy. Soc . Edinburgh. To be published. ATKINSON, F. AND FULTON, C. 1999. Asymptotics of the Titchmarsh-Weyl m-coefficient for non-integrable potentials. Proc. Roy. Soc. Edinburgh. To be published."},{"issue":"59","key":"e_1_2_1_5_1","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1112\/plms\/s3-59.2.294","article-title":"Spectral asymptotics for Sturm-Liouville equations","volume":"3","author":"BENNEWITZ C.","year":"1989","unstructured":"BENNEWITZ , C. 1989 . Spectral asymptotics for Sturm-Liouville equations . Proc. London Math. Soc. 3 , 59 , 294 - 338 . BENNEWITZ, C. 1989. Spectral asymptotics for Sturm-Liouville equations. Proc. London Math. Soc. 3, 59, 294-338.","journal-title":"Proc. London Math. Soc."},{"key":"e_1_2_1_6_1","volume-title":"Linear Operators, Part H: Spectral Theory","author":"DUNFORD N.","unstructured":"DUNFORD , N. AND SCHWARTZ , J. 1963. Linear Operators, Part H: Spectral Theory . John Wiley & amp; Sons, Inc., New York, NY. DUNFORD, N. AND SCHWARTZ, J. 1963. Linear Operators, Part H: Spectral Theory. John Wiley & Sons, Inc., New York, NY."},{"key":"e_1_2_1_7_1","first-page":"51","article-title":"Parametrizations of Titchmarsh's m(~)-functions in the limit circle case","volume":"229","author":"FULTON C.","year":"1977","unstructured":"FULTON , C. 1977 . Parametrizations of Titchmarsh's m(~)-functions in the limit circle case . Trans. AMS 229 , 51 - 63 . FULTON, C. 1977. Parametrizations of Titchmarsh's m(~)-functions in the limit circle case. Trans. AMS 229, 51-63.","journal-title":"Trans. AMS"},{"key":"e_1_2_1_8_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0308210500012312","article-title":"Singular eigenvalue problems with eigenvalue parameter contained in the boundary condition","volume":"87","author":"FULTON C.","year":"1980","unstructured":"FULTON , C. 1980 . Singular eigenvalue problems with eigenvalue parameter contained in the boundary condition . Proc. Roy. Soc. Edinburgh 87A , 1 - 34 . FULTON, C. 1980. Singular eigenvalue problems with eigenvalue parameter contained in the boundary condition. Proc. Roy. Soc. Edinburgh 87A, 1-34.","journal-title":"Proc. Roy. Soc. Edinburgh"},{"key":"e_1_2_1_9_1","first-page":"163","article-title":"An integral equation iterative scheme for asymptotic expansions of spectral quantities of regular Sturm-Liouville problems","volume":"4","author":"FULTON C.","year":"1982","unstructured":"FULTON , C. 1982 . An integral equation iterative scheme for asymptotic expansions of spectral quantities of regular Sturm-Liouville problems . J. Integral Eq. 4 , 163 - 172 . FULTON, C. 1982. An integral equation iterative scheme for asymptotic expansions of spectral quantities of regular Sturm-Liouville problems. J. Integral Eq. 4, 163-172.","journal-title":"J. Integral Eq."},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1006\/jmaa.1994.1429","article-title":"Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems","volume":"188","author":"FULTON C.","year":"1994","unstructured":"FULTON , C. AND PRUESS , S. 1994 . Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems . J. Math. Anal. Appl. 188 , 297 - 340 . FULTON, C. AND PRUESS, S. 1994. Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems. J. Math. Anal. Appl. 188, 297-340.","journal-title":"J. Math. Anal. Appl."},{"key":"e_1_2_1_11_1","unstructured":"FULTON C. PRUESS S. AND XIE Y. 1999. The automatic classification of Sturm-Liouville problems. Appl. Math. Comput. To be published. FULTON C. PRUESS S. AND XIE Y. 1999. The automatic classification of Sturm-Liouville problems. Appl. Math. Comput. 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A simplified proof of the expansion theorem for singular second order differential equations . Duke Math. J. 18 , 57 - 71 . LEVINSON, N. 1951. A simplified proof of the expansion theorem for singular second order differential equations. Duke Math. J. 18, 57-71.","journal-title":"Duke Math. J."},{"key":"e_1_2_1_14_1","volume-title":"Expansion in Characteristic Functions of Differential Equations of the Second Order. Gosthekhizdat","author":"LEVITAN B.","unstructured":"LEVITAN , B. 1950. Expansion in Characteristic Functions of Differential Equations of the Second Order. Gosthekhizdat , Moscow, Russia . In Russian . LEVITAN, B. 1950. Expansion in Characteristic Functions of Differential Equations of the Second Order. Gosthekhizdat, Moscow, Russia. 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Ann."}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/285861.285867","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,31]],"date-time":"2022-12-31T09:17:01Z","timestamp":1672478221000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/285861.285867"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,3]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,3]]}},"alternative-id":["10.1145\/285861.285867"],"URL":"http:\/\/dx.doi.org\/10.1145\/285861.285867","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":["Applied Mathematics","Software"],"published":{"date-parts":[[1998,3]]},"assertion":[{"value":"1998-03-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}