Complex Planar Splines.
Abstract
In contradistinction to the known theory on complex splines which are defined on the boundary of a region and then extended into the interior by Cauchy's integral formula. We define complex planar splines on a region itself as a complex valued continuous function which is defined piece-wise on suitable meshes of that region. The main idea is to use non-holomorphic functions as pieces, since holomorphic pieces would lead to just one holomorphic function on the whole region by a well known identity theorem in the theory of functions in one complex variable. Some of the techniques used are available from the theory of finite elements. But also are considered new aspects, namely mapping properties of a complex planar spline v and the difference f - v where f is in general a holomorphic function. For triangular, rectangular, parallelogram meshes and meshes on circular sectors, explicit expressions are provided and also properties of the newly introduced complex planar splines are studied.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1981
- Accession Number
- ADA100849
Entities
People
- Gerhard Opfer
- Madan L. Puri
Organizations
- Indiana University Bloomington