(1799 - 1891)

Eminente naturalista, publicó el Compendio de Geografía de la Isla de Cuba, primer libro de su tipo escrito e impreso en el país. Pero su obra monumental es Ictiología Cubana, fruto de sus investigaciones de más de cincuenta años.

Natural and Exact Sciences

2000 | Problems of Rienman contour in complex and hypercomplex analysis

Main executives entity: University of Holguín (1)

Other entities: University of Oriente

Main author: Ricardo Abreu Blaya, del (1).

Coauthors: Juan Bory Reyes, from (2)

Summary:

The softness properties of Cauchy-type integral are demonstrated over a maximal class of closed Jordan rectifiable curves that characterizes the singular integral operator's invariance relative to Holder generalized spaces, and it is proven the compactness property of the operator switch on regular Ahlfors curves.

It is obtained the explicit solution of two problems of Riemann contour, generalized for analytic functions by means of a reduction process to classic Riemann problems. It was determined a formula for the calculation of the number of lineally independent solutions of the respective homogeneous problems. For the first time, these problems are solved in a maximal class of closed Jordan curves. It is extended to the hypercomplex case a technique to solve Riemann contour problems that does not use the integration on domains’ frontiers, which allows studying this problem for the case of non-rectifiable and even fractal surfaces. It is obtained an explicit solution of an analogous of Riemann-Hilbert's compound problem for monogenic quaternion functions on non-soft surfaces. It is demonstrated a unit existence theorem of the solutions of Riemann contour problem with non-constant coefficient for monogenic functions on soft surfaces.

The use of Clifford's Algebras is a very important area in multiple applications of physics-mathematics. /p>

There are presented 10 publications about original results in specialized magazines, 6 of them very prestigious and specific. Another valuable contribution is the work published in the volume dedicated to Clifford Analysis by BirkhÑ¤user Publishing House.

The authors have taken their results to important international events of this specialty.

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