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  • 1 Department of Applied Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest H-1117, Hungary
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Abstract

The notions of parallel sum and parallel difference of two nonnegative forms were introduced and studied by Hassi, Sebestyén, and de Snoo in [13] and [14]. In this paper we consider the parallel subtraction with much circumstances. Criteria are established for the solvability of the equation with an unknown when and are given. We identify as the minimal solution, and characterize all the solutions under the assumption where λ>1. The Galois correspondence induced by the map is also studied. We show that if the equation is solvable, then there is a unique -closed solution, namely . Finally, we consider some extremal problems such as the extreme points of the interval , and the characterization of the minimal forms in terms of the parallel sum.

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