Recent Topics on Frame Theory

Frame theory is recently an active research area in mathematics, computer science, and engineering with many exciting applications in a variety of different ¿elds. They are generalizations of bases in Hilbert spaces. Frames for Hilbert spaces were ¿rst introduced in 1952 by Dün and Schae¿er for study of nonharmonic Fourier series. They were reintroduced and developed in 1986 by Daubechies, Grossmann and Meyer, and popularized from then on. Hilbert C*-modules is a generalization of Hilbert spaces by allowing the inner product to take values in a C*-algebra rather than in the ¿eld of complex numbers. The aim of this book is to collect a selection of elementary, essentially and recently subjects on frame theory in Hilbert space and Hilbert C*-module. For this, we divide this book by two self-contained parts. In part I, we investigate frame theory in Hilbert space and in part II, we study frame theory in Hilbert C*-module.