Search Results - "Brackx, F"

The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis by Brackx, F., De Schepper, H., Lávička, R., Souček, V.

“…As is the case for the theory of holomorphic functions in the complex plane, the Cauchy Integral Formula has proven to be a cornerstone of Clifford analysis,…”
Get full text

Fischer Decomposition for Massless Fields of Spin 1 in Dimension 4 by Brackx, F., De Schepper, H., Krump, L., Souček, V.

“…The massless field equations for lower integer and half-integer values of spin in Minkowski space are fundamental equations in mathematical physics. Their…”
Get full text

The Cauchy–Kovalevskaya extension theorem in Hermitian Clifford analysis by Brackx, F., De Schepper, H., Lávička, R., Souček, V.

“…Hermitian Clifford analysis is a higher dimensional function theory centered around the simultaneous null solutions, called Hermitian monogenic functions, of…”
Get full text

A matrix Hilbert transform in Hermitean Clifford analysis by Brackx, F., De Knock, B., De Schepper, H.

“…Orthogonal Clifford analysis is a higher dimensional function theory offering both a generalization of complex analysis in the plane and a refinement of…”
Get full text

Harmonic and monogenic potentials in low dimensional Euclidean half-space by Brackx, F., De Bie, H., De Schepper, H.

“…In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space Rm+1 was constructed recently,…”
Get full text

Fundaments of quaternionic Clifford analysis II: splitting of equations by Brackx, F., De Schepper, H., Eelbode, D., Lávička, R., Souček, V.

“…Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional function theory which refines harmonic analysis and…”
Get full text

A Hermitian Cauchy formula on a domain with fractal boundary by Abreu-Blaya, R., Bory-Reyes, J., Brackx, F., De Schepper, H., Sommen, F.

“…Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the…”
Get full text

Fischer decomposition in symplectic harmonic analysis by Brackx, F., De Schepper, H., Eelbode, D., Lávička, R., Souček, V.

“…In the framework of quaternionic Clifford analysis in Euclidean space R 4 p , which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the…”
Get full text

Gel'fand-Tsetlin bases of orthogonal polynomials in Hermitean Clifford analysis by Brackx, F., De Schepper, H., Lávička, R., Souček, V.

“…An explicit algorithmic construction is given for orthogonal bases for spaces of homogeneous polynomials, in the context of Hermitean Clifford analysis, which…”
Get full text

Hardy spaces of solutions of generalized Riesz and Moisil-Teodorescu systems by Brackx, F., Delanghe, R., De Schepper, H.

“…Hardy spaces of solutions of generalized Riesz and generalized Moisil-Teodorescu systems in half space , and of their non-tangential L 2 -boundary values in ℝ…”
Get full text

The Teodorescu Operator in Clifford Analysis by Brackx, F., De Schepper, H., Luna-Elizarrarás, M. E., Shapiro, M.

“…Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued…”
Get full text

On conjugate harmonic functions in Euclidean space by Brackx, F. F., Delanghe, R., Sommen, F. C.

“…In this paper we consider the problem of constructing in domains Ωof ℝm+1 with a specific geometric property, a conjugate harmonic V to a given harmonic…”
Get full text

Two-index Clifford–Hermite polynomials with applications in wavelet analysis by Brackx, F., De Schepper, H., De Schepper, N., Sommen, F.

“…Clifford analysis may be regarded as a higher-dimensional analogue of the theory of holomorphic functions in the complex plane. It has proven to be an…”
Get full text

HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS by BRACKX, F., DE SCHEPPER, H.

“…Around the central theme of """square root""" of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow…”
Get full text

Differential forms versus multi-vector functions in Hermitean Clifford analysis by Brackx, F, De Schepper, H, Sou<img src="http:/fbpe/img, V

“…Similarities are shown between the algebras of complex differential forms and of complex Clifford algebra-valued multi-vector functions in an open region of…”
Get full text

239P The association between disease severity and utilities, mental health, fatigue, sleep disturbances and sick leave in patients with myasthenia gravis by Brackx, F., Goffart, B., Linthoudt, T., De Ruyck, F., Phillips, G., Dewilde, S., Claeys, K.

“…Myasthenia gravis (MG) is a rare autoimmune disorder associated with muscle weakness and fatigue. MG-ADL is a questionnaire assessing the impact of MG symptoms…”
Get full text

Clifford algebra-valued orthogonal polynomials in Euclidean space by Brackx, F., De Schepper, N., Sommen, F.

“…In this paper a new method for constructing Clifford algebra-valued orthogonal polynomials in Euclidean space is presented. In earlier research, only…”
Get full text

Clifford-hermite wavelets in euclidean space by Brackx, F., Sommen, F.

Get full text

The Mehler Formula for the Generalized Clifford–Hermite Polynomials by Brackx, F., de Schepper, N., Kou, K. I., Sommen, F.

“…The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional Fractional Fourier transform. In this paper, we…”
Get full text

SPHERICAL MEANS, DISTRIBUTIONS AND CONVOLUTION OPERATORS IN CLIFFORD ANALYSIS by BRACKX, F., DELANGHE, R., SOMMEN, F.

“…New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work,…”
Get full text