Weighted affine density

Abstract

In this chapter we introduce the notion of weighted affine density for multiple weighted sequences in the affine group. We study its basic properties, which will be used in the subsequent chapters. Then we discuss the notion of affine density introduced by Sun and Zhou [119] and study the exact relation to the affine density we will employ in this book. This chapter contains a generalization of the notion of weighted affine density as introduced by Heil and Kutyniok in [73] to multiple weighted sequences. Further, some of the results in this chapter generalize the results obtained in Kutyniok [92] to multiple weighted sequences.