Hypercomplex Analysis Selected Topics

More documents

Recommendations

Info

[15] F. Brackx, B. De Knock, H. De Schepper, F. Sommen, On Cauchy and Martinelli-Bochner Formulae in Hermitean Clifford Analysis, Bull. Braz. Math. Soc. 40 (3), 2009, 395-416. [16] F. Brackx, B. De Knock, H. De Schepper, A matrix Hilbert transform in Hermitean Clifford Analysis, J. Math. Anal. Appl. 344 (2), 2008, 1068-1078. [17] F. Brackx, R. Delanghe and F. Sommen, Clifford analysis, Pitman, London, 1982. [18] F. Brackx, H. De Schepper, N. De Schepper, F. Sommen, Hermitean Clifford- Hermite polynomials, Adv. Appl. Clifford Alg. 17 (3), 2007, 311-330. [19] F. Brackx, H. De Schepper, D. Eelbode, V. Souček, The Howe Dual Pair in Hermitean Clifford Analysis, Rev. Mat. Iberoamericana 26 (2010)(2), 449-479. [20] F. Brackx, H. De Schepper, R. Lávička, V. Souček, The Cauchy-Kovalevskaya Extension Theorem in Hermitean Clifford Analysis, J. Math. Anal. Appl. 381 (2011), 649-660. [21] F. Brackx, H. De Schepper, R. Lávička, V. Souček, Fischer decompositions of kernels of Hermitean Dirac operators, In: Proceedings of ICNAAM 2010, Rhodes, Greece, 2010 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1281 (2010), pp. 1484-1487. [22] F. Brackx, H. De Schepper, R. Lávička, V. Souček, Gel’fand-Tsetlin procedure for the construction of orthogonal bases in Hermitean Clifford analysis, In: Proceedings of ICNAAM 2010, Rhodes, Greece, 2010 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1281 (2010), pp. 1508-1511. [23] F. Brackx, H. De Schepper, R. Lávička, V. Souček, Orthogonal basis of Hermitean monogenic polynomials: an explicit construction in complex dimension 2, In: Proceedings of ICNAAM 2010, Rhodes, Greece, 2010 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1281 (2010), pp. 1451-1454. [24] F. Brackx, H. De Schepper, F. Sommen, The Hermitian Clifford analysis toolbox, Adv. Appl. Cliff. Alg. 18 (3-4), 2008, 451-487. [25] F. Brackx, H. De Schepper, F. Sommen, A Theoretical Framework for Wavelet Analysis in a Hermitean Clifford Setting, Communications on Pure and Applied Analysis 6 (3), 2007, 549-567. [26] F. Brackx, H. De Schepper, V. Souček, Fischer decompositions in Euclidean and Hermitean Clifford analysis, Arch. Math. (Brno) 46 (5), 2010, 301-321. [27] J. Bureš, R. Lávička and V. Souček, Elements of Quaternionic Analysis and Radon Transform, Textos de Matematica, vol. 42, Universidade de Coimbra, Coimbra, 2009. [28] I. Cação, Constructive approximation by monogenic polynomials, PhD thesis, Univ. Aveiro, 2004. [29] I. Cação, Complete orthonormal sets of polynomial solutions of the Riesz and Moisil-Teodorescu systems in R 3 , Numer. Algor. 55 (2010), 191-203. [30] I. Cação, K. Gürlebeck, H. R. Malonek, Special monogenic polynomials and L2-approximation, Adv. Appl. Cliff. Alg. 11 (2001) (S2), 47-60. [31] I. Cação, K. Gürlebeck, S. Bock, Complete orthonormal systems of spherical monogenics - a constructive approach, In Methods of Complex and Clifford Analysis, Son LH, Tutschke W, Jain S (eds). Proceedings of ICAM, Hanoi, SAS International Publications, 2004. [32] I. Cação, K. Gürlebeck, S. Bock, On derivatives of spherical monogenics, Complex Var. Elliptic Equ. 51 (2006) (811), 847-869. 50
[33] I. Cação and H. R. Malonek, Remarks on some properties of monogenic polynomials, ICNAAM 2006. International conference on numerical analysis and applied mathematics 2006 (T.E. Simos, G. Psihoyios, and Ch. Tsitouras, eds.), Wiley-VCH, Weinheim, 2006, pp. 596-599. [34] I. Cação and H. R. Malonek, On a complete set of hypercomplex Appell polynomials, Proc. ICNAAM 2008, (T. E. Timos, G. Psihoyios, Ch. Tsitouras, Eds.), AIP Conference Proceedings 1048, 647-650. [35] J. Cnops, Reproducing kernels of spaces of vector valued monogenics, Adv. appl. Clifford alg. 6 1996 (2), 219-232. [36] A. Damiano and D. Eelbode, Invariant Operators Between Spaces of h- Monogenic Polynomials, Adv. Appl. Cliff. Alg. 19 (2), 2009, 237-251. [37] F. Colombo, I. Sabadini, F. Sommen, D. C. Struppa, Analysis of Dirac Systems and Computational Algebra, Birkhäuser, Boston, 2004. [38] R. Delanghe, On regular-analytic functions with values in a Clifford algebra, Math. Ann. 185 (1970), 91-111. [39] R. Delanghe, Clifford Analysis: History and Perspective, Comput. Methods Funct. Theory 1 (2001) (1), 107-153. [40] R. Delanghe, On homogeneous polynomial solutions of the Riesz system and their harmonic potentials, Complex Var. Elliptic Equ. 52 (2007) (10-11), 1047- 1061. [41] R. Delanghe, On homogeneous polynomial solutions of the Moisil-Théodoresco system in R 3 , Comput. Methods Funct. Theory 9 (2009) (1), 199-212. [42] R. Delanghe, On homogeneous polynomial solutions of generalized Moisil- Théodoresco systems in Euclidean space, CUBO 12 (2010), 145-167. [43] R. Delanghe, F. Sommen, V. Souček, Clifford Algebra and Spinor-valued Functions, Mathematics and Its Applications 53, Kluwer Academic Publishers, 1992. [44] R. Delanghe, R. Lávička and V. Souček, On polynomial solutions of generalized Moisil-Théodoresco systems and Hodge-de Rham systems, Adv. appl. Clifford alg. 21 (2011), 521-530. [45] R. Delanghe, R. Lávička and V. Souček, The Fischer decomposition for Hodgede Rham systems in Euclidean spaces, to appear in Math. Methods Appl. Sci. [46] R. Delanghe, R. Lávička and V. Souček, The Howe duality for Hodge systems, In: Proceedings of 18th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering (ed. K. Gürlebeck and C. Könke), Bauhaus-Universität Weimar, Weimar, 2009. [47] P. A. M. Dirac, The quantum theory of the electron, Proc. Roy. Soc. A 117 (1928), 610-624. [48] D. Eelbode, Stirling numbers and Spin-Euler polynomials, Exp. Math. 16 (2007) (1), 55-66. [49] D. Eelbode, Irreducible sl(m)-modules of Hermitean monogenics, Complex Var. Elliptic Equ. 53 (2008) (10), 975-987. [50] D. Eelbode, Fu Li He, Taylor series in Hermitean Clifford Analysis, Compl. Anal. Oper. Theory, DOI: 10.1007/s11785-009-0036-y. [51] M. I. Falcão, J. F. Cruz and H. R. Malonek, Remarks on the generation of monogenic functions, Proc. of the 17-th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering, ISSN 1611-4086 (K. Gürlebeck and C. Könke, eds.), Bauhaus- University Weimar, 2006. 51
Page 1: Hypercomplex Analysis Selected Topi
Page 4 and 5: [L6] Canonical bases for sl(2,C)-mo
Page 6 and 7: mannian manifolds and the correspon
Page 8 and 9: considered as a Gelfand-Tsetlin bas
Page 11 and 12: Chapter 2 Preliminaries of hypercom
Page 13 and 14: 3.2, we construct an orthogonal bas
Page 15 and 16: By linearity, we extend the so-call
Page 17 and 18: complex structure J. Let us note th
Page 19 and 20: Chapter 3 Complete orthogonal Appel
Page 21 and 22: for some complex coefficients tk,µ
Page 23 and 24: with x = x1e1 + · · · + xm−1em
Page 25 and 26: where Λ(W ) is the exterior algebr
Page 27 and 28: In fact, we have constructed a comp
Page 29 and 30: M0 M1 M2 · · · ∂z 〈 ˆ f 2 0
Page 31 and 32: with β s,m k = −(k + m − s)/(k
Page 33 and 34: (b) Each function g ∈ L2 (Bm, C
Page 35 and 36: H 1 0 H 1 1 H 1 2 v− e3 v+ g1
Page 37 and 38: Then the Hermitian Cauchy-Kovalevsk
Page 39 and 40: Chapter 4 Finely monogenic function
Page 41 and 42: (FH1) f has a finely continuous fin
Page 43 and 44: Theorem 18. If U ⊂ R 2 is a finel
Page 45: that λ m+1 (Vn \ V ) → 0 as n
Page 49: Bibliography [1] R. Abłamowicz and
Page 53 and 54: [71] N. Gürlebeck, On Appell Sets

Hypercomplex Analysis Selected Topics

Create successful ePaper yourself

Delete template?

Save as template?