In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems.
A convolution operator, bounded on , is bounded on , with the same operator norm, if and are conjugate exponents. It is well known that this fact is false if we replace with a general non-commutative locally compact group . In this paper we give a simple construction of a convolution operator on a suitable compact group , wich is bounded on for every and is unbounded on if .
We prove a formula relating the index of a solution and the rotation number of a certain complex vector along bifurcation diagrams.
It is known that the vector stop operator with a convex closed characteristic of class is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping is Lipschitz continuous on the boundary of . We prove that in the regular case, this condition is also necessary.
We give an example of uniformly rotund in every direction space for which the minimal displacement characteristic is maximal.
If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by [...] We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.
Let denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space into itself. Given , we define the elementary operator by . In this paper we study the class of operators which have the following property: implies for all trace class operators . Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of is closed under taking...
In the paper a new proof of Lemma 11 in the above-mentioned paper is given. Its original proof was based on Theorem 3 which has been shown to be incorrect.