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- W2953084904 abstract "We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward the boundary of D, and p is a holomorphic self-map of D such that the weighted composition operator W assigning the product of m and the composition of f and p to a given function f is compact on a holomorphic functional Hilbert space (containing the polynomial functions densely) on D with reproducing kernel K blowing up along the diagonal of D toward its boundary, then p has a unique fixed point in D. We apply this result by making a reasonable conjecture about the spectrum of W based on previous one-variable and multivariable results concerning compact weighted and unweighted composition operators." @default.
- W2953084904 created "2019-06-27" @default.
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- W2953084904 date "2005-12-02" @default.
- W2953084904 modified "2023-09-27" @default.
- W2953084904 title "Compact weighted composition operators and fixed points in convex domains" @default.
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