Recent Topics on Frame Theory
In Hilbert space and Hilbert C*-module
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Frame theory is recently an active research area in mathematics, computer science, and engineering with many exciting applications in a variety of different fields. They are generalizations of bases in Hilbert spaces. Frames for Hilbert spaces were first introduced in 1952 by Du n 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 field of complex...
Frame theory is recently an active research area in mathematics, computer science, and engineering with many exciting applications in a variety of different fields. They are generalizations of bases in Hilbert spaces. Frames for Hilbert spaces were first introduced in 1952 by Du n 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 field 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.
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