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Zoltán Sebestyén
Zoltán Sebestyén
Department of Applied Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest H-1117, Hungarye-mail: sebesty@cs.elte.hu
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Tamás Titkos
Tamás Titkos
Department of Applied Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest H-1117, Hungarye-mail: sebesty@cs.elte.hu
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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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| Acta Mathematica Hungarica | |
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