{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T16:07:18Z","timestamp":1757779638649},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"S1","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T00:00:00Z","timestamp":1702512000000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bol. Soc. Mat. Mex."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct a set of quaternionic metamonogenic functions (that is, in <jats:inline-formula><jats:alternatives><jats:tex-math>$${{\\,\\textrm{Ker}\\,}}(D+\\lambda )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mrow>\n                      <mml:mspace \/>\n                      <mml:mtext>Ker<\/mml:mtext>\n                      <mml:mspace \/>\n                    <\/mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>D<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mi>\u03bb<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for diverse real <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bb<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>) in the unit disk, such that every metamonogenic function is approximable in the quaternionic Hilbert module <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of the disk. The set is orthogonal except for the small subspace of elements of orders zero and one. These functions are used to express time-dependent solutions of the imaginary-time wave equation in the polar coordinate system.<\/jats:p>","DOI":"10.1007\/s40590-023-00557-5","type":"journal-article","created":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T02:02:00Z","timestamp":1702519320000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quaternionic metamonogenic functions in the unit disk"],"prefix":"10.1007","volume":"29","author":[{"given":"J.","family":"Morais","sequence":"first","affiliation":[]},{"given":"R.","family":"Michael Porter","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,14]]},"reference":[{"issue":"1\u20134","key":"557_CR1","first-page":"177","volume":"14","author":"M Abul-Ez","year":"1990","unstructured":"Abul-Ez, M., Constales, D.: Basic sets of polynomials in Clifford analysis. Complex Var. 14(1\u20134), 177\u2013185 (1990)","journal-title":"Complex Var."},{"key":"557_CR2","doi-asserted-by":"crossref","unstructured":"Bock, S., G\u00fcrlebeck, K., L\u00e1vi\u010dka, R., Sou\u010dek, V.: The Gelfand\u2013Tsetlin bases for spherical monogenics in dimension $$3$$. Rev. Mat. Iberoam. 28(4), 1165\u20131192 (2012)","DOI":"10.4171\/rmi\/708"},{"key":"557_CR3","unstructured":"Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. Pitman Advanced Publishing Program (1982)"},{"key":"557_CR4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511535055","volume-title":"Classical Covariant Fields","author":"M Burgess","year":"2002","unstructured":"Burgess, M.: Classical Covariant Fields. Cambridge University Press, Cambridge (2002)"},{"issue":"2\u20133","key":"557_CR5","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s11075-010-9411-z","volume":"55","author":"I Ca\u00e7\u00e3o","year":"2010","unstructured":"Ca\u00e7\u00e3o, I.: Complete orthonormal sets of polynomial solutions of the Riesz and Moisil\u2013Teodorescu systems in $${\\mathbb{R} }^3$$. Numer. Algorithms 55(2\u20133), 191\u2013203 (2010)","journal-title":"Numer. Algorithms"},{"key":"557_CR6","doi-asserted-by":"crossref","unstructured":"Ca\u00e7\u00e3o, I., Falc\u00e3o, M.I., Malonek, H.: Laguerre derivative and monogenic Laguerre polynomials: an operational approach. Math. Comput. Model. 53, 1084\u20131094 (2011)","DOI":"10.1016\/j.mcm.2010.11.071"},{"issue":"10\u201311","key":"557_CR7","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1080\/17476930701466630","volume":"52","author":"R Delanghe","year":"2007","unstructured":"Delanghe, R.: On homogeneous polynomial solutions of the Riesz system and their harmonic potentials. Complex Var. Ellipt. Equ. 52(10\u201311), 1047\u20131062 (2007)","journal-title":"Complex Var. Ellipt. Equ."},{"issue":"1","key":"557_CR8","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/BF03321722","volume":"9","author":"R Delanghe","year":"2009","unstructured":"Delanghe, R.: On Homogeneous polynomial solutions of the Moisil\u2013Th\u00e9odoresco system in $${\\mathbb{R} }^3$$. Comput. Methods Funct. Theory 9(1), 199\u2013212 (2009)","journal-title":"Comput. Methods Funct. Theory"},{"key":"557_CR9","unstructured":"Fueter, R.: Regul\u00e4re Funktionen einer Quaternionenvariablen, Lecture Notes, Spring Semester. Math. Inst. Univ. Z\u00fcrich (1940)"},{"key":"557_CR10","unstructured":"Fueter, R.: Functions of a Hyper Complex Variable. Lecture Notes Written and Supplemented by E. Bareiss, Fall Semester. Math. Inst. Univ. Z\u00fcrich (1949)"},{"key":"557_CR11","doi-asserted-by":"publisher","first-page":"125","DOI":"10.4171\/zaa\/186","volume":"5","author":"K G\u00fcrlebeck","year":"1986","unstructured":"G\u00fcrlebeck, K.: Hypercomplex factorization of the Hemholtz equation. Zeitschrift f\u00fcr Analysis und ihre Anwendungen 5, 125\u2013131 (1986)","journal-title":"Zeitschrift f\u00fcr Analysis und ihre Anwendungen"},{"key":"557_CR12","doi-asserted-by":"publisher","DOI":"10.1515\/9783112576182","volume-title":"Quaternionic Analysis and Elliptic Boundary Value Problems","author":"K G\u00fcrlebeck","year":"1989","unstructured":"G\u00fcrlebeck, K., Spr\u00f6\u00dfig, W.: Quaternionic Analysis and Elliptic Boundary Value Problems. Akademie Verlag, Berlin (1989)"},{"key":"557_CR13","volume-title":"Quaternionic Calculus for Engineers and Physicists","author":"K G\u00fcrlebeck","year":"1997","unstructured":"G\u00fcrlebeck, K., Spr\u00f6\u00dfig, W.: Quaternionic Calculus for Engineers and Physicists. Wiley, Chichester (1997)"},{"key":"557_CR14","volume-title":"Holomorphic Functions in the Plane and $$n$$-Dimensional Space","author":"K G\u00fcrlebeck","year":"2008","unstructured":"G\u00fcrlebeck, K., Habetha, K., Spr\u00f6\u00dfig, W.: Holomorphic Functions in the Plane and $$n$$-Dimensional Space. Birkh\u00e4user Verlag, Berlin (2008)"},{"key":"557_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0964-1","volume-title":"Application of Holomorphic Functions in Two and Higher Dimensions","author":"K G\u00fcrlebeck","year":"2016","unstructured":"G\u00fcrlebeck, K., Habetha, K., Spr\u00f6\u00dfig, W.: Application of Holomorphic Functions in Two and Higher Dimensions. Birkh\u00e4user Verlag, Berlin (2016)"},{"key":"557_CR16","volume-title":"Lectures on Quaternions. Containing a Systematic Statement of a New Mathematical Method","author":"WR Hamilton","year":"1853","unstructured":"Hamilton, W.R.: Lectures on Quaternions. Containing a Systematic Statement of a New Mathematical Method. Hodges and Smith, Grafton-Street, Dublin (1853)"},{"key":"557_CR17","volume-title":"Handbook of Mathematical Formulas and Integrals","author":"A Jeffrey","year":"2008","unstructured":"Jeffrey, A., Dai, H.-H.: Handbook of Mathematical Formulas and Integrals, 4th edn. Elsevier, Amsterdam (2008)","edition":"4"},{"key":"557_CR18","volume-title":"Applied Quaternionic Analysis. Research and Exposition in Mathematics, vol. 28","author":"V Kravchenko","year":"2003","unstructured":"Kravchenko, V.: Applied Quaternionic Analysis. Research and Exposition in Mathematics, vol. 28. Heldermann Verlag, Lemgo (2003)"},{"key":"557_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-0862-4_19","volume-title":"Clifford Analysis and Its Applications. NATO Science Series","author":"H Leutwiler","year":"2001","unstructured":"Leutwiler, H.: Quaternionic analysis in $${\\mathbb{R} }^3$$ versus its hyperbolic modification. In: Brackx, F., Chisholm, J.S.R., Soucek, V. (eds.) Clifford Analysis and Its Applications. NATO Science Series, vol. 25. Springer, Dordrecht (2001). https:\/\/doi.org\/10.1007\/978-94-010-0862-4_19"},{"issue":"9","key":"557_CR20","doi-asserted-by":"publisher","first-page":"1080","DOI":"10.1002\/mma.2665","volume":"36","author":"ME Luna-Elizarrar\u00e1s","year":"2013","unstructured":"Luna-Elizarrar\u00e1s, M.E., P\u00e9rez-de la Rosa, M.A., Rodr\u00edguez-Dagnino, R.M., Shapiro, M.: On quaternionic analysis for the Schr\u00f6dinger operator with a particular potential and its relation with the Mathieu functions. Math. Methods Appl. Sci. 36(9), 1080\u20131094 (2013)","journal-title":"Math. Methods Appl. Sci."},{"key":"557_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0622-0","volume-title":"Real Quaternionic Calculus Handbook","author":"J Morais","year":"2014","unstructured":"Morais, J., Georgiev, S., Spr\u00f6\u00dfig, W.: Real Quaternionic Calculus Handbook. Birkh\u00e4user, Basel (2014)"},{"key":"557_CR22","unstructured":"Morais, J.: A Quaternionic Version Theory Related to Spheroidal Functions, Habilitation thesis, TU Bergakademie Freiberg (2021)"},{"key":"557_CR23","doi-asserted-by":"crossref","unstructured":"Morais, J., Porter, R.M.: Reduced-quaternionic Mathieu functions, time-dependent Moisil\u2013Teodorescu operators, and the imaginary-time wave equation. Appl. Math. Comput. 38, 1\u201319 (2023), 127588","DOI":"10.1016\/j.amc.2022.127588"},{"key":"557_CR24","unstructured":"Petrovsky, I.G.: Lectures on Partial Differential Equations. Translated from the Russian by A. Shenitzer. Interscience Publishers, New York (1954)"},{"key":"557_CR25","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1017\/S0305004100055638","volume":"85","author":"A Sudbery","year":"1979","unstructured":"Sudbery, A.: Quaternionic analysis. Math. Proc. Camb. Philos. Soc. 85, 199\u2013225 (1979)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"557_CR26","volume-title":"On Metaharmonic Functions, Lecture Notes on TICMI","author":"I Vekua","year":"2013","unstructured":"Vekua, I.: On Metaharmonic Functions, Lecture Notes on TICMI, vol. 14. Tbilisi University Press, Tbilisi (2013)"}],"container-title":["Bolet\u00edn de la Sociedad Matem\u00e1tica Mexicana"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40590-023-00557-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40590-023-00557-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40590-023-00557-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T11:34:18Z","timestamp":1712835258000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40590-023-00557-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12]]},"references-count":26,"journal-issue":{"issue":"S1","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["557"],"URL":"https:\/\/doi.org\/10.1007\/s40590-023-00557-5","relation":{},"ISSN":["1405-213X","2296-4495"],"issn-type":[{"value":"1405-213X","type":"print"},{"value":"2296-4495","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12]]},"assertion":[{"value":"17 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 December 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"100"}}