{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T23:44:46Z","timestamp":1773791086144,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2003,7,1]],"date-time":"2003-07-01T00:00:00Z","timestamp":1057017600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,7,1]],"date-time":"2003-07-01T00:00:00Z","timestamp":1057017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Computational Mathematics"],"published-print":{"date-parts":[[2003,7]]},"DOI":"10.1023\/a:1022862704316","type":"journal-article","created":{"date-parts":[[2003,4,4]],"date-time":"2003-04-04T21:57:10Z","timestamp":1049493430000},"page":"159-182","source":"Crossref","is-referenced-by-count":3,"title":["Orthogonal Systems of Singular Functions and Numerical Treatment of Problems with Degeneration of Data"],"prefix":"10.1007","volume":"19","author":[{"given":"Alexei","family":"Bespalov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5112626_CR1","series-title":"Regional Conference Series in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970470","volume-title":"Orthogonal Polynomials and Special Functions","author":"R. Askey","year":"1975","unstructured":"R. Askey, Orthogonal Polynomials and Special Functions, Regional Conference Series in Applied Mathematics, Vol. 21 (SIAM, Philadelphia, PA, 1975)."},{"key":"5112626_CR2","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1137\/0724049","volume":"24","author":"I. Babu\u0161ka","year":"1987","unstructured":"I. Babu\u0161ka and M. Suri, The optimal convergence rate of the p-version of the finite element method, SIAM J. Numer. Anal. 24 (1987) 750\u2013776.","journal-title":"SIAM J. Numer. Anal."},{"key":"5112626_CR3","volume-title":"Relativistic Quantum Theory","author":"V.B. Berestetskii","year":"1971","unstructured":"V.B. Berestetskii, E.M. Lifshitz and L.P. Pitaevskii, Relativistic Quantum Theory (Pergamon Press, New York, 1971)."},{"key":"5112626_CR4","unstructured":"A.Y. Bespalov and V.A. Rukavishnikov, The investigation of a certain class of functions with degeneration in the boundary strip, in: Methods of Numerical Analysis (Collected Papers), Part 2, ed. V.A. Rukavishnikov (Dalnauka, Vladivostok, 1995) (in Russian) pp. 77\u201388."},{"key":"5112626_CR5","first-page":"201","volume":"4","author":"A.Y. Bespalov","year":"2001","unstructured":"A.Y. Bespalov and V.A. Rukavishnikov, The use of singular functions in the h-p version of the finite element method for the Dirichlet problem with degeneration of the input data, Siberian J. Numer. Math. 4 (2001) 201\u2013228.","journal-title":"Siberian J. Numer. Math."},{"key":"5112626_CR6","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"1978","unstructured":"P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amsterdam, 1978)."},{"key":"5112626_CR7","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1137\/0721073","volume":"21","author":"M.R. Dorr","year":"1984","unstructured":"M.R. Dorr, The approximation theory for the p-version of the finite element method, SIAM J. Numer. Anal. 21 (1984) 1180\u20131207.","journal-title":"SIAM J. Numer. Anal."},{"key":"5112626_CR8","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1006\/jmaa.1998.6025","volume":"226","author":"B.-Y. Guo","year":"1998","unstructured":"B.-Y. Guo, Gegenbauer approximation and its applications to differential equations on the whole line, J. Math. Anal. Appl. 226 (1998) 180\u2013206.","journal-title":"J. Math. Anal. Appl."},{"key":"5112626_CR9","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1006\/jmaa.1999.6677","volume":"243","author":"B.-Y. Guo","year":"2000","unstructured":"B.-Y. Guo, Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations, J. Math. Anal. Appl. 243 (2000) 373\u2013408.","journal-title":"J. Math. Anal. Appl."},{"key":"5112626_CR10","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/S0168-9274(01)00039-3","volume":"38","author":"B.-Y. Guo","year":"2001","unstructured":"B.-Y. Guo, Gegenbauer approximation and its applications to differential equations with rough asymptotic behaviors at infinity, Appl. Numer. Math. 38 (2001) 403\u2013425.","journal-title":"Appl. Numer. Math."},{"key":"5112626_CR11","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF00298636","volume":"1","author":"B. Guo","year":"1986","unstructured":"B. Guo and I. Babu\u0161ka, The h-p version of the finite element method. Part 1: The basic approximation results, Comp. Mech. 1 (1986) 21\u201341.","journal-title":"Comp. Mech."},{"key":"5112626_CR12","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1023\/A:1016681018268","volume":"14","author":"B.-Y. Guo","year":"2001","unstructured":"B.-Y. Guo and W. Li-lian, Jacobi interpolation approximations and their applications to singular differential equations, Adv. Comput. Math. 14 (2001) 227\u2013276.","journal-title":"Adv. Comput. Math."},{"key":"5112626_CR13","volume-title":"Inequalities","author":"G.H. Hardy","year":"1952","unstructured":"G.H. Hardy, J.E. Littlewood and G. P\u00f3lya, Inequalities (Cambridge Univ. Press, Cambridge, 1952)."},{"key":"5112626_CR14","volume-title":"Elements of the Theory of Functions and Functional Analysis","author":"A.N. Kolmogorov","year":"1968","unstructured":"A.N. Kolmogorov and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1968) (in Russian)."},{"key":"5112626_CR15","volume-title":"Quantum Mechanics: Non-Relativistic Theory","author":"L.D. Landau","year":"1977","unstructured":"L.D. Landau and E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Pergamon Press, New York, 1977)."},{"key":"5112626_CR16","volume-title":"Partial Differential Equations","author":"V.P. Mikhailov","year":"1976","unstructured":"V.P. Mikhailov, Partial Differential Equations (Nauka, Moscow, 1976) (in Russian)."},{"key":"5112626_CR17","first-page":"1318","volume":"309","author":"V.A. Rukavishnikov","year":"1989","unstructured":"V.A. Rukavishnikov, On differentiability properties of an R\n\u03bd-generalized solution of the Dirichlet problem, Dokl. Akad. Nauk SSSR 309 (1989) 1318\u20131320; English transl. in Soviet Math. Dokl. 40 (1990).","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"5112626_CR18","first-page":"447","volume":"337","author":"V.A. Rukavishnikov","year":"1994","unstructured":"V.A. Rukavishnikov, The Dirichlet problem with incompatible degeneration of initial data, Dokl. Russian Acad. Nauk 337 (1994) 447\u2013449; English transl. in Russian Acad. Sci. Dokl.Math. 50 (1995) 104\u2013107.","journal-title":"Dokl. Russian Acad. Nauk"},{"key":"5112626_CR19","first-page":"171","volume":"2","author":"V.A. Rukavishnikov","year":"1999","unstructured":"V.A. Rukavishnikov and E.V. Kashuba, On the properties of an orthonormalized singular polynomials set, Siberian J. Numer. Math. 2 (1999) 171\u2013183.","journal-title":"Siberian J. Numer. Math."},{"key":"#cr-split#-5112626_CR20.1","unstructured":"V.A. Rukavishnikov and H.I. Rukavishnikova, The finite element method for the first boundary value problem with compatible degeneracy of the initial data, Dokl. Russian Akad. Nauk 338 (1994) 731-733"},{"key":"#cr-split#-5112626_CR20.2","unstructured":"English transl. in Russian Acad. Sci. Dokl. Math. 50 (1995) 335-339."},{"key":"5112626_CR21","first-page":"540","volume-title":"ENUMATH 97, Proc.of the 2nd European Conf.on Numerical Mathematics and Advanced Applications","author":"V.A. Rukavishnikov","year":"1998","unstructured":"V.A. Rukavishnikov and H.I. Rukavishnikova, The finite element method for the third boundary value problem with strong singularity of solution, in: ENUMATH 97, Proc.of the 2nd European Conf.on Numerical Mathematics and Advanced Applications, eds. R. Rannacher et al. (World Scientific, Singapore, 1998) pp. 540\u2013548."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1022862704316.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1022862704316\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1022862704316.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T23:20:23Z","timestamp":1747437623000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1022862704316"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7]]},"references-count":22,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2003,7]]}},"alternative-id":["5112626"],"URL":"https:\/\/doi.org\/10.1023\/a:1022862704316","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,7]]}}}