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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Closed form solutions to polynomial operator equations

To the best of my knowledge the problem at hand is a generalisation of monic matrix polynomials. Can a closed form solution to the following equation be found, $$u_3A_3X^3B_3 + u_2A_2X^2B_2 + u_1A_1XB …