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A note on a one-parameter family of non-symmetric number triangles

Falcao M. I., Malonek H. R.

Opuscula Mathematica

2012

Vol. 32, no. 4

661-673

The recent growing interest in special Clifford algebra valued polynomial solutions of generalized Cauchy-Riemann systems in (n + 1)-dimensional Euclidean spaces suggested a detailed study of the arithmetical properties of their coefficients, due to their combinatoric relevance. This concerns, in particular, a generalized Appell sequence of homogeneous polynomials whose coefficient set can be treated as a one-parameter family of non-symmetric triangles of fractions. The discussion of its properties, similar to those of the ordinary Pascal triangle (which itself does not belong to the family), is carried out in this paper.

W2,kCln-best aproximatiion of a γ-regular function

Lakew D. A.

Journal of Applied Analysis

2007

Vol. 13, nr 2

259-273

Is this paper, we construct a γ-regular Cln-minimal function systems in W2,kΓ (Ω,Cln ∩ker Dγ(Ω,Cln), the generalized Bergman space of Cln-valued functions in the Sobolev space W2,kΓ (Ω) which are used in the best way to approximate null solutions of the inhomogeneous Direc operator.