Abstract

A Function Space Approach to Spectral Related Problems

T. Venkatesh1 and Karuna Samaje*2

1Professor, Department of Mathematics, Rani Channamma University, Belagavi, Karnataka, INDIA. *2Research Scholar, Department of Mathematics, Rani Channamma University, Belagavi, Karnataka, INDIA.

ABSTRACT

In this exposition we have considered the orthonormal basis of square integrable functions on 𝐿2(ℝ𝑛) and give group transformations relating to the two types of maps viz. That are Translations and Dilations. These notions have spectral connections to the Laplacian operator, which we have studied in our subsequent work.

Keywords :Orthonormal basis, Translations, Dilations, Laplacian operator.

map1 map2 map3