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A solution of an infinite system of quadratic equations in reproducing kernel space. (English) Zbl 1136.46024

Summary: We introduce several operators in certain reproducing kernel Hilbert spaces, and we use them in the solution of a general family of quadratic equations in an infinite number of variables. We further describe an approximation scheme with quadratic polynomials for solving these equations.

MSC:

46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
46N20 Applications of functional analysis to differential and integral equations
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