A note on higher order Dirac operators in Clifford analysis
-
Daniel Alfonso Santiesteban
Abstract
In the framework of Clifford analysis, we study higher order Dirac operators constructed with k-vectors. We find a necessary and sufficient condition to determine whether a function cancels them.
Funding source: Consejo Nacional de Humanidades, Ciencias y Tecnologías
Award Identifier / Grant number: 1043969
Funding statement: This work was partially supported by Postgraduate Study Fellowship of the Consejo Nacional de Humanidades, Ciencias y Tecnologías (CONAHCYT) (grant number 1043969).
References
[1] R. Abreu Blaya, D. Alfonso Santiesteban, J. Bory Reyes and A. Moreno García, Inframonogenic decomposition of higher-order Lipschitz functions, Math. Methods Appl. Sci. 45 (2022), no. 9, 4911–4928. 10.1002/mma.8078Search in Google Scholar
[2] R. Abreu Blaya, J. Bory Reyes, A. Guzmán Adán and U. Kähler, On the Π-operator in Clifford analysis, J. Math. Anal. Appl. 434 (2016), no. 2, 1138–1159. 10.1016/j.jmaa.2015.09.038Search in Google Scholar
[3] D. Alfonso Santiesteban and R. Abreu Blaya, Isomorphisms of partial differential equations in Clifford analysis, Adv. Appl. Clifford Algebr. 32 (2022), no. 1, Paper No. 10. 10.1007/s00006-021-01191-ySearch in Google Scholar
[4]
D. Alfonso Santiesteban, R. Abreu Blaya and M. P. Árciga Alejandre,
On a generalized Lamé–Navier system in
[5]
D. Alfonso Santiesteban, R. Abreu Blaya and M. P. Árciga Alejandre,
On
[6] D. Alfonso Santiesteban, R. A. Blaya and J. B. Reyes, Boundary value problems for a second-order elliptic partial differential equation system in Euclidean space, Math. Methods Appl. Sci. 46 (2023), no. 14, 15784–15798. 10.1002/mma.9426Search in Google Scholar
[7]
D. Alfonso Santiesteban, Y. P. Pérez and R. A. Blaya,
Generalizations of harmonic functions in
[8] F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Res. Notes Math. 76, Pitman, Boston, 1982. Search in Google Scholar
[9] R. Delanghe, F. Sommen and V. Souček, Clifford Algebra and Spinor-Valued Functions, Math. Appl. 53, Kluwer Academic, Dordrecht, 1992. 10.1007/978-94-011-2922-0Search in Google Scholar
[10] D. C. Dinh, On structure of inframonogenic functions, Adv. Appl. Clifford Algebr. 31 (2021), no. 3, Paper No. 50. 10.1007/s00006-021-01157-0Search in Google Scholar
[11] A. M. García, T. Moreno García, R. Abreu Blaya and J. Bory Reyes, A Cauchy integral formula for inframonogenic functions in Clifford analysis, Adv. Appl. Clifford Algebr. 27 (2017), no. 2, 1147–1159. 10.1007/s00006-016-0745-zSearch in Google Scholar
[12] K. Gürlebeck and H. M. Nguyen, ψ-Hyperholomorphic functions and an application to elasticity problems, AIP Conf. Proc. 1648 (2015), Article ID 440005. 10.1063/1.4912656Search in Google Scholar
[13] R. Lávička, The Fischer decomposition for the H-action and its applications, Hypercomplex analysis and applications, Trends Math., Birkhäuser/Springer, Basel (2011), 139–148. 10.1007/978-3-0346-0246-4_10Search in Google Scholar
[14] L.-W. Liu and H.-K. Hong, Clifford algebra valued boundary integral equations for three-dimensional elasticity, Appl. Math. Model. 54 (2018), 246–267. 10.1016/j.apm.2017.09.031Search in Google Scholar
[15] H. R. Malonek, D. Peña Peña and F. Sommen, Fischer decomposition by inframonogenic functions, Cubo 12 (2010), no. 2, 189–197. 10.4067/S0719-06462010000200012Search in Google Scholar
[16] A. Moreno García, D. Alfonso Santiesteban and R. Abreu Blaya, On the Dirichlet problem for second order elliptic systems in the ball, J. Differential Equations 364 (2023), 498–520. 10.1016/j.jde.2023.03.050Search in Google Scholar
[17] A. Moreno García, T. Moreno García, R. Abreu Blaya and J. Bory Reyes, Inframonogenic functions and their applications in 3-dimensional elasticity theory, Math. Methods Appl. Sci. 41 (2018), no. 10, 3622–3631. 10.1002/mma.4850Search in Google Scholar
[18] K. Nōno, On the quaternion linearization of Laplacian Δ, Bull. Fukuoka Univ. Ed. III 35 (1985), 5–10. Search in Google Scholar
[19]
R. M. Porter, M. V. Shapiro and N. L. Vasilevski,
On the analogue of the
[20] M. Shapiro, On the conjugate harmonic functions of M. Riesz–E. Stein–G. Weiss, Topics in Complex Analysis, Differential Geometry and Mathematical Physics (St. Konstantin 1996), World Scientific, River Edge (1997), 8–32. Search in Google Scholar
[21] M. V. Shapiro, On some boundary-value problems for functions with values in Clifford algebra, Mat. Vesnik 40 (1988), no. 3–4, 321–326. Search in Google Scholar
[22] M. V. Shapiro and N. L. Vasilevski, Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems. I. ψ-hyperholomorphic function theory, Complex Variables Theory Appl. 27 (1995), no. 1, 17–46. 10.1080/17476939508814803Search in Google Scholar
[23] L. Wang, S. Jia, L. Luo and F. Qiu, Plemelj formula of inframonogenic functions and their boundary value problems, Complex Var. Elliptic Equ. 68 (2023), no. 7, 1158–1181. 10.1080/17476933.2022.2040019Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings
Articles in the same Issue
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings
