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- W2029946444 abstract "We define here a degree theory for proper analytic Fredholm maps of index zero defined on open subsets of complex Banach spaces, and we prove that the standard properties for a degree theory hold. Our approach avoids the differential geometry tools used by Elworthy and Tromba [8] in similar work. We prove that for analytic maps the degree theory defined by Nussbaum in [11,13] agrees with ours, and similarly Browder and Gupta's degree theory in [3] is a special case of ours. If is an analytic Fredholm map of index zero defined on an open subset of the complexification of a real Banach space B,if commutes with complex conjugation, and if is compact for some , then if N is the number of points in (mod 2). Under further assumptions on and y (see Theorem 10 below), deg and deg (mod 2). Our results generalize some recent work of Jane Cronin [6][7]." @default.
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- W2029946444 date "1971-07-01" @default.
- W2029946444 modified "2023-10-17" @default.
- W2029946444 title "Estimates for the number of solutions of operator equations" @default.
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- W2029946444 doi "https://doi.org/10.1080/00036817108839013" @default.
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