Picture of athlete cycling

Open Access research with a real impact on health...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

Explore open research content by Physical Activity for Health...

Eigenfunction expansions for generalized functions of several variables

Lamb, W. and McGhee, D.F. (2004) Eigenfunction expansions for generalized functions of several variables. Integral Transforms and Special Functions, 15 (3). pp. 239-249. ISSN 1065-2469

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

The constructive method developed by Zemanian [Zemanian, A. H. (1968). Generalized Integral Transformations. Interscience, New York] for extending L2-convergence results on eigenfunction expansions to certain classes of generalized functions of one variable is shown to be valid also for generalized functions of several variables. In the latter case, the expansions involve the eigenfunctions associated with symmetric partial differential operators. Specific examples considered are the Laplace-Beltrami operator on the unit sphere in ℝN and a class of symmetric elliptic operators in L2(Φ#169;), where Φ#169; is a bounded region in ℝN. Applications to the solution of distributional initial-boundary value problems are also discussed.