Cuong, Dao Viet; Son, Le Hung Some new results for function theory in hypercomplex analysis with parameters. (English) Zbl 1468.30084 Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 37, 16 p. (2021). Summary: In this paper we study a generalization of Clifford algebra depending on parameters introduced by W. Tutschke and C. J. Vanegas [in: Some topics on value distribution and differentiability in complex and \(p\)-adic analysis. Beijing: Science Press., 430–450 (2008; Zbl 1232.30034)]. We also introduce some related notions, a Cauchy-Pompeiu integral formula, and two boundary value problems for monogenic functions with values in this Clifford algebra. MSC: 30G35 Functions of hypercomplex variables and generalized variables 30E25 Boundary value problems in the complex plane Keywords:Clifford algebra depending on a parameter; Cauchy-Pompeiu formula, boundary value problems Citations:Zbl 1232.30034 PDFBibTeX XMLCite \textit{D. V. Cuong} and \textit{L. H. Son}, Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 37, 16 p. (2021; Zbl 1468.30084) Full Text: DOI References: [1] Alayon-Solarz, D.; Vanegas, CJ, Operators associated to the Cauchy-Riemann operators in elliptic complex numbers, Adv. Appl. Clifford Algebras, 22, 257-270 (2012) · Zbl 1271.30022 · doi:10.1007/s00006-011-0306-4 [2] Alayon-Solarz, D., Vanegas, C.J.: The Cauchy-Pompeiu representation formula in elliptic complex numbers. Complex Var. Elliptic Equations 57(9), 1025-1033 (2012) · Zbl 1254.30051 [3] Baderko, E.A.: Some Schauder estimates. In Analysis, numerics and applications of differential and integral equations (Stuttgart, 1996), vol. 379 of Pitman Res. Notes Math. Ser., pp. 22-24. Longman, Harlow (1998) · Zbl 0901.35012 [4] Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. In: Pitman Research Notes in Mathematics, vol. 76. Pitman Advanced Publishing Program, London (1982) · Zbl 0529.30001 [5] Doan Cong Dinh, Dirichlet boundary value problem for monogenic function in Clifford analysis, Complex Var. Elliptic Equations, 59, 9, 1201-1213 (2014) · Zbl 1295.35186 · doi:10.1080/17476933.2013.823162 [6] Gilbarg, D.; Trudinger, NS, Elliptic Partial Differential Equations of Second Order (1983), Berlin, Heidelbaerg, New York, Tokyo: Springer, Berlin, Heidelbaerg, New York, Tokyo · Zbl 0562.35001 [7] Gilbert, George T., Positive definite matrices and Sylvester’s criterion, Math. Assoc. Am., 98, 1, 44-46 (1991) · Zbl 0741.15011 · doi:10.1080/00029890.1991.11995702 [8] Giorgi, G.: Various proofs of the Sylvester criterion for quadratic forms. J. Math. Res. (2017). doi:10.5539/jmr.v9n6p55 [9] Hamilton, WE, Elements of Quaternion (1866), London: Longmans, Green & Co, London [10] Miranda, C.: Partial differential equations of elliptic type. Ergebnisse der Mathematik und ihrer Grenzgebiete. Band 2. Springer, New York (1970) (Second revised edition. Translated from the Italian by Zane C. Motteler) [11] Schauder, J., Über lineare elliptische Dierentialgleichungen zweiter Ordnung, Math. Z., 38, 257-282 (1934) · Zbl 0008.25502 · doi:10.1007/BF01170635 [12] Tutschke, W., The Distinguishing Boundary for Monogenic Functions of Clifford Analysis, Adv. Appl. Clifford Algebras, 25, 441-451 (2015) · Zbl 1319.30041 · doi:10.1007/s00006-014-0484-y [13] Tutschke, W., Vanegas, C.J.: Clifford algebras depending on parameters and their applications to partial differential equations. In: Escassut, A., Tutschke, W., Yang, C.C. (eds.) Chapter 14 in Some Topics on Value Distributrion and Differentiability in Complex and P-adic Analysis, pp. 430-450. Science Press, Beijing (2008) · Zbl 1232.30034 [14] Tutschke, W.; Vanegas, CJ, A boundary value problem for monogenic functions in parameterdepending Clifford algebras, Complex Var. Elliptic Equations Int. J., 56, 1-4, 113-118 (2011) · Zbl 1213.35182 · doi:10.1080/17476930903394762 [15] Yaglom, IM, Complex Numbers in Geometry (1968), New York: Academic Press, New York · Zbl 0147.20201 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.