Time and band limiting for matrix valued functions: an integral and a commuting differential operator
نویسندگان
چکیده
We extend to a situation involving matrix valued orthogonal polynomials and matrix valued spherical functions on the sphere a result that goes back to work of Claude Shannon in lying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing in a non-commutative setup that a bispectral property implies that the corresponding integral operator of “time and band limiting” admits a commuting differential operator. This is an analog of the famous prolate spheroidal wave operator, but now all operators act on matrix valued functions.
منابع مشابه
Time and band limiting for matrix valued functions
The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing...
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