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Linear representations of SU(2) described by using Kravchuk polynomials

We show that a new unitary transform with characteristics almost similar to those of the finite Fourier transform can be defined in any finite-dimensional Hilbert space. It is defined by using the Kravchuk polynomials, and we call it Kravchuk transform. Some of its properties are investigated and used in order to obtain a simple alternative description for the irreducible representations of the Lie algebra su(2) and group SU(2). Our approach offers a deeper insight into the structure of the linear representations of SU(2) and new possibilities of computation, very useful in applications in quantum mechanics, quantum information, signal and image processing.