{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T08:21:00Z","timestamp":1726042860544},"publisher-location":"Cham","reference-count":46,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030267476"},{"type":"electronic","value":"9783030267483"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-26748-3_7","type":"book-chapter","created":{"date-parts":[[2019,8,28]],"date-time":"2019-08-28T16:22:28Z","timestamp":1567009348000},"page":"93-115","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One"],"prefix":"10.1007","author":[{"given":"Helmuth R.","family":"Malonek","sequence":"first","affiliation":[]},{"given":"Isabel","family":"Ca\u00e7\u00e3o","sequence":"additional","affiliation":[]},{"given":"M. Irene","family":"Falc\u00e3o","sequence":"additional","affiliation":[]},{"given":"Gra\u00e7a","family":"Tomaz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,29]]},"reference":[{"issue":"1","key":"7_CR1","doi-asserted-by":"publisher","first-page":"163","DOI":"10.2307\/2373431","volume":"90","author":"EM Stein","year":"1968","unstructured":"Stein, E.M., Weiss, G.: Generalization of the Cauchy-Riemann equations and representations of the rotation group. Am. J. Math. 90(1), 163\u2013196 (1968)","journal-title":"Am. J. Math."},{"issue":"7\u20138","key":"7_CR2","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1080\/17476933.2011.609930","volume":"57","author":"F Brackx","year":"2012","unstructured":"Brackx, F., Delanghe, R., De Schepper, H.: Hardy spaces of solutions of generalized Riesz and Moisil-Teodorescu systems. Complex Var. Elliptic Equ. 57(7\u20138), 771\u2013785 (2012)","journal-title":"Complex Var. Elliptic Equ."},{"key":"7_CR3","first-page":"142","volume":"5","author":"G Moisil","year":"1931","unstructured":"Moisil, G., Teodorescu, N.: Functions holomorphes dans l\u2019espace. Mathematica Cluj 5, 142\u2013159 (1931)","journal-title":"Mathematica Cluj"},{"key":"7_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2922-0","volume-title":"Clifford Algebra and Spinor-Valued Functions","author":"R. Delanghe","year":"1992","unstructured":"Delanghe,\u00a0R., Sommen,\u00a0F., Sou\u010dek,\u00a0V.: Clifford algebra and spinor-valued functions. A function theory for the Dirac operator. Mathematics and its Applications, vol. 53. Kluwer Academic Publishers, Dordrecht (1992)"},{"issue":"7","key":"7_CR5","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1002\/mma.1563","volume":"35","author":"R Delanghe","year":"2012","unstructured":"Delanghe, R., L\u00e1vi\u010dka, R., Sou\u010dek, V.: The Gelfand\u2013Tsetlin bases for Hodge\u2013de Rham systems in Euclidean spaces Math. Methods Appl. Sci. 35(7), 745\u2013757 (2012)","journal-title":"Methods Appl. Sci."},{"key":"7_CR6","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/BF01359699","volume":"185","author":"R Delanghe","year":"1970","unstructured":"Delanghe, R.: On regular-analytic functions with values in a Clifford Algebra. Math. Ann. 185, 91\u2013111 (1970)","journal-title":"Math. Ann."},{"key":"7_CR7","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/BF01199562","volume":"8","author":"R Fueter","year":"1935","unstructured":"Fueter, R.: \u00dcber die analytische Darstellung der regul\u00e4ren Funktionen einer Quaternionenvariablen Comm. Math. Helvetici 8, 371\u2013378 (1935). https:\/\/doi.org\/10.1007\/BF01199562","journal-title":"Math. Helvetici"},{"unstructured":"Kravchenko, V.V.: Applied quaternionic analysis. Research and Experience in Mathematics, vol. 28, Heldermann Verlag, Lemgo (2003)","key":"7_CR8"},{"issue":"1","key":"7_CR9","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/BF03320981","volume":"1","author":"R Delanghe","year":"2001","unstructured":"Delanghe, R.: Clifford analysis: history and perspective. Comput. Methods Funct. Theory 1(1), 107\u2013153 (2001)","journal-title":"Comput. Methods Funct. Theory"},{"key":"7_CR10","volume-title":"\u00dcber Funktionen einer Quaternionenvariablen","author":"R Fueter","year":"1928","unstructured":"Fueter, R.: \u00dcber Funktionen einer Quaternionenvariablen. Atti Congr. Int. Mat, Bologna (1928)"},{"issue":"S2","key":"7_CR11","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF03219133","volume":"11","author":"Helmuth R. Malonek","year":"2001","unstructured":"Malonek, H.: Rudolf Fueter and his motivation for hypercomplex function theory. Adv. Appl. Clifford Algebr. 11(S2), 219\u2013230 (2001)","journal-title":"Advances in Applied Clifford Algebras"},{"unstructured":"Fueter,\u00a0R.: Functions of a hyper complex variable. Manuscript of Lecture Notes, Fall Semester 1948\/49, written and supplemented by E. Bareiss, ETH Bibliothek Z\u00fcrich, 318p (1950)","key":"7_CR12"},{"key":"7_CR13","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, Basel (2008)"},{"key":"7_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7295-9","volume-title":"Quaternionic Analysis and Elliptic Boundary Value Problems","author":"Klaus G\u00fcrlebeck","year":"1990","unstructured":"G\u00fcrlebeck,\u00a0K., Spr\u00f6\u00dfig,\u00a0W.: Quaternionic analysis and elliptic boundary value problems. International Series of Numerical Mathematics, vol. 89, Birkh\u00e4user-Verlag, Basel (1990)"},{"key":"7_CR15","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1080\/00036818208839388","volume":"13","author":"J Ryan","year":"1982","unstructured":"Ryan, J.: Clifford analysis with generalize elliptic and quasi-elliptic functions. Appl. Anal. 13, 151\u2013171 (1982)","journal-title":"Appl. Anal."},{"key":"7_CR16","volume-title":"Clifford Analysis","author":"F Brackx","year":"1982","unstructured":"Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. Pitman, Boston, London, Melbourne (1982)"},{"key":"7_CR17","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1080\/17476939008814401","volume":"14","author":"H Malonek","year":"1990","unstructured":"Malonek, H.: A new hypercomplex structure of the Euclidean space $$\\mathbb{R}^{n+1}$$ and a concept of hypercomplex differentiability. Complex Variables, Theory Appl. 14, 25\u201333 (1990)","journal-title":"Complex Variables, Theory Appl."},{"unstructured":"Malonek,\u00a0H.: The concept of hypercomplex differentiability and related differential forms. In: K\u00fchnau, R., Tutschke, W. (eds.) Studies in Complex Analysis and its Applications to Partial Differential Equations 1, vol. 256, pp. 193\u2013202. Pitman , Longman (1991)","key":"7_CR18"},{"doi-asserted-by":"crossref","unstructured":"Malonek,\u00a0H.: Hypercomplex derivability\u2014The characterization of monogenic functions in $${\\mathbb{R}}^{n+1}$$ by their derivative. In: Ryan, J. et al. (eds.) Clifford Algebras and their Applications in Mathematical Physics, vol. 2. Progress in Physics, vol. 19, Birkh\u00e4user (2000)","key":"7_CR19","DOI":"10.1007\/978-1-4612-1374-1_15"},{"unstructured":"Malonek,\u00a0H.R.: Selected topics in hypercomplex function theory. In: Eriksson,\u00a0S.-L. (ed.) Clifford Algebras and Potential Theory. Report Series 7, University of Joensuu, pp. 111\u2013150 (2004)","key":"7_CR20"},{"key":"7_CR21","first-page":"199","volume":"39","author":"K G\u00fcrlebeck","year":"1999","unstructured":"G\u00fcrlebeck, K., Malonek, H.: A hypercomplex derivative of monogenic functions in $$\\mathbb{R}^{n+1}$$ and its applications. Complex Var. Theory Appl. 39, 199\u2013228 (1999)","journal-title":"Complex Var. Theory Appl."},{"unstructured":"Ryan,\u00a0J.: Clifford algebras in analysis and related topics. Studies in Advanced Mathematics, CRC PRESS (1996)","key":"7_CR22"},{"doi-asserted-by":"crossref","unstructured":"Pompeiu,\u00a0M.: Sur une classe de fonctions d\u00fane variable complexe. Rend. Circ. Mat. Palermo 33, 108\u2013 113 (1912), 35, 277\u2013281 (1913)","key":"7_CR23","DOI":"10.1007\/BF03015292"},{"issue":"2","key":"7_CR24","doi-asserted-by":"publisher","first-page":"119","DOI":"10.24033\/asens.186","volume":"9","author":"P Appell","year":"1880","unstructured":"Appell, P.: Sur une classe de polyn\u00f4mes. Ann. Sci. \u00c9cole Norm. Sup. 9(2), 119\u2013144 (1880)","journal-title":"Ann. Sci. \u00c9cole Norm. Sup."},{"unstructured":"Mitrea,\u00a0M., Sabac,\u00a0F.: Pompeiu\u2019s integral representation formula. History and Mathematics. Rev. Roumaine Math. Pures Appl. 43, 211\u2013226 (1998)","key":"7_CR25"},{"key":"7_CR26","volume-title":"Advanced Calculus: A Differential Forms Approach","author":"HE Edwards","year":"1993","unstructured":"Edwards, H.E.: Advanced Calculus: A Differential Forms Approach, 3rd edn. Birkh\u00e4user, Boston, Basel, Berlin (1993)","edition":"3"},{"unstructured":"Malonek,\u00a0H.: On the concept of holomorphy in higher dimensions\u2014Hypercomplex differentiability and series in permutative powers. Habilitation thesis, Halle (1987)","key":"7_CR27"},{"key":"7_CR28","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. Phil. Soc. 85, 199\u2013225 (1979)","journal-title":"Math. Proc. Camb. Phil. Soc."},{"key":"7_CR29","first-page":"181","volume":"15","author":"H Malonek","year":"1990","unstructured":"Malonek, H.: Power series representation for monogenic functions in $$\\mathbb{R}^{n+1}$$ basead on a permutational product. Complex Var. Theory Appl. 15, 181\u2013191 (1990)","journal-title":"Complex Var. Theory Appl."},{"key":"7_CR30","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1090\/S0002-9904-1945-08437-7","volume":"51","author":"IM Sheffer","year":"1945","unstructured":"Sheffer, I.M.: Note on Appell polynomials. Bull. Am. Math. Soc. 51, 739\u2013744 (1945)","journal-title":"Bull. Am. Math. Soc."},{"issue":"6","key":"7_CR31","doi-asserted-by":"publisher","first-page":"2133","DOI":"10.1090\/S0002-9939-2010-10648-2","volume":"139","author":"DW Lee","year":"2011","unstructured":"Lee, D.W.: On multiple Appell polynomials. Proc. Am. Math. Soc. 139(6), 2133\u20132141 (2011)","journal-title":"Proc. Am. Math. Soc."},{"issue":"6","key":"7_CR32","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1080\/10652469.2015.1013035","volume":"26","author":"L Aceto","year":"2015","unstructured":"Aceto, L., Malonek, H.R., Tomaz, G.: A unified matrix approach to the representation of Appell polynomials. Integral Transf. Spec. Funct. 26(6), 426\u2013441 (2015)","journal-title":"Integral Transf. Spec. Funct."},{"doi-asserted-by":"crossref","unstructured":"Malonek,\u00a0H.R., Falc\u00e3o,\u00a0M.I.: Special monogenic polynomials\u2014properties and applications. In: Simos,\u00a0T.S., Psihoyios,\u00a0G., Tsitouras,\u00a0C. (eds.) AIP Conference Proceedings, vol. 936, pp. 765\u2013767 (2007)","key":"7_CR33","DOI":"10.1063\/1.2790265"},{"issue":"5\u20136","key":"7_CR34","doi-asserted-by":"publisher","first-page":"1084","DOI":"10.1016\/j.mcm.2010.11.071","volume":"53","author":"I Ca\u00e7\u00e3o","year":"2011","unstructured":"Ca\u00e7\u00e3o, I., Falc\u00e3o, M.I., Malonek, H.R.: Laguerre derivative and monogenic Laguerre polynomials: an operational approach. Math. Comput. Model. 53(5\u20136), 1084\u20131094 (2011)","journal-title":"Math. Comput. Model."},{"issue":"4","key":"7_CR35","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1002\/mma.1213","volume":"33","author":"S Bock","year":"2010","unstructured":"Bock, S., G\u00fcrlebeck, K.: On a generalized Appell system and monogenic power series. Math. Methods Appl. Sci. 33(4), 394\u2013411 (2010)","journal-title":"Math. Methods Appl. Sci."},{"issue":"4","key":"7_CR36","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1007\/s00006-012-0330-z","volume":"22","author":"D Eelbode","year":"2012","unstructured":"Eelbode, D.: Monogenic Appell sets as representations of the Heisenberg algebra. Adv. Appl. Clifford Algebra 22(4), 1009\u20131023 (2012)","journal-title":"Adv. Appl. Clifford Algebra"},{"key":"7_CR37","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s11785-011-0200-z","volume":"6","author":"R L\u00e0vi\u010dka","year":"2012","unstructured":"L\u00e0vi\u010dka, R.: Complete orthogonal Appell systems for spherical monogenics. Complex Anal. Oper. Theory 6, 477\u2013489 (2012)","journal-title":"Complex Anal. Oper. Theory"},{"issue":"4","key":"7_CR38","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.4171\/RMI\/708","volume":"28","author":"S Bock","year":"2012","unstructured":"Bock, S., G\u00fcrlebeck, K., L\u00e0vi\u010dka, R., Sou\u010dek, V.: Gelfand-Tstelin bases for spherical monogenics in dimension 3. Rev. Mat. Iberuom. 28(4), 1165\u20131192 (2012)","journal-title":"Rev. Mat. Iberuom."},{"issue":"2","key":"7_CR39","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/BF03321833","volume":"12","author":"I Ca\u00e7\u00e3o","year":"2012","unstructured":"Ca\u00e7\u00e3o, I., Falc\u00e3o, M.I., Malonek, H.R.: Matrix representations of a basic polynomial sequence in arbitrary dimension. Comput. Methods Funct. Theory 12(2), 371\u2013391 (2012)","journal-title":"Comput. Methods Funct. Theory"},{"key":"7_CR40","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s00006-015-0596-z","volume":"27","author":"I Ca\u00e7\u00e3o","year":"2017","unstructured":"Ca\u00e7\u00e3o, I., Falc\u00e3o, M.I., Malonek, H.R.: Three term recurrence relations for systems of Clifford algebra-valued polynomial sequences. Adv. Appl. Clifford Algebras 27, 71\u201385 (2017)","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"7_CR41","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.apnum.2016.07.006","volume":"116","author":"L Aceto","year":"2017","unstructured":"Aceto, L., Malonek, H.R., Tomaz, G.: Matrix approach to hypercomplex Appell polynomials. Appl. Numer. Math. 116, 2\u20139 (2017)","journal-title":"Appl. Numer. Math."},{"doi-asserted-by":"publisher","unstructured":"Ca\u00e7\u00e3o,\u00a0I., Falc\u00e3o,\u00a0M.I., Malonek,\u00a0H.R.: Combinatorial identities in the context of hypercomplex function theory. AIP Conference Proceedings 1978, 280004-1-280004-4 (2018). https:\/\/doi.org\/10.1063\/1.5043904","key":"7_CR42","DOI":"10.1063\/1.5043904"},{"key":"7_CR43","doi-asserted-by":"publisher","first-page":"1723","DOI":"10.1002\/mma.2931","volume":"37","author":"C Cruz","year":"2014","unstructured":"Cruz, C., Falc\u00e3o, M.I., Malonek, H.R.: Monogenic pseudo-complex power functions and their applications. Math. Methods Appl. Sci. 37, 1723\u20131735 (2014)","journal-title":"Math. Methods Appl. Sci."},{"key":"7_CR44","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1007\/s00025-012-0259-5","volume":"63","author":"D Pe\u00f1a Pe\u00f1a","year":"2013","unstructured":"Pe\u00f1a Pe\u00f1a, D.: Shifted Appell sequences in Clifford analysis. Results Math. 63, 1145\u20131157 (2013)","journal-title":"Results Math."},{"key":"7_CR45","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1007\/s11785-017-0649-5","volume":"11","author":"I Ca\u00e7\u00e3o","year":"2017","unstructured":"Ca\u00e7\u00e3o, I., Falc\u00e3o, M.I., Malonek, H.R.: Hypercomplex polynomials, Vietoris\u2019 rational numbers and a related integer numbers sequence. Complex Anal. Oper. Theory 11, 1059\u20131076 (2017)","journal-title":"Complex Anal. Oper. Theory"},{"unstructured":"Ca\u00e7\u00e3o,\u00a0I., Falc\u00e3o,\u00a0M.I., Malonek,\u00a0H.R., Tomaz,\u00a0G.: Combinatorial identities associated with a multidimensional polynomial sequence. J. Integer Seq. 21(7), 18.7.4 (2018)","key":"7_CR46"}],"container-title":["Springer Proceedings in Mathematics & Statistics","Modern Methods in Operator Theory and Harmonic Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-26748-3_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,17]],"date-time":"2021-01-17T15:57:46Z","timestamp":1610899066000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-26748-3_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030267476","9783030267483"],"references-count":46,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-26748-3_7","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"29 August 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"OTHA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Scientific Conference (on) Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Rostov-on-Don","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Russia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 April 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 April 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"otha2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/otha.sfedu.ru\/conf2018\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}