Hilbert Spaces

Abstract

In this chapter, we study a special class of Banach space in which the underlying vector space is equipped with a structure, called an inner product or a scalar product providing the generalization of geometrical concepts like angle and orthogonally between two vectors. The inner product is nothing but a generalization of the dot product of vector calculus. Hilbert space method is a powerful tool to tackle problems of diverse fields of classical mathematics like linear equations, variational methods, approximation theory, differential equations.