Bases in hilbert spaces

This chapter tries to collect some basic facts for Riesz basis with simple introduction nature. These facts are minimal for understanding the applications in later chapters. These include basis property of exponential family e^int, which is also referred to as nonharmonic Fourier series; the property of entire functions, specially for entire function of exponential type; the materials about the Hardy space and Blaschke are only limited to a few results; The D-type operator and One-rank perturbation for D-type operator are also introduced. The materials of generalized divided difference (GDD) developed by Russian school is also introduced. The Pavlov theorem and Keldysh theorem are specially introduced.