منابع مشابه
On Commuting Differential Operators
The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...
متن کاملOn multilinear operators commuting with Lie derivatives
Let E 1, . . . , Ek and E be natural vector bundles defined over the category Mf m of smooth oriented m–dimensional manifolds and orientation preserving local diffeomorphisms, with m ≥ 2. Let M be an object of Mf m which is connected. We give a complete classification of all separately continuous k–linear operators D : Γc(E1M) × . . . × Γc(EkM) → Γ(EM) defined on sections with compact supports,...
متن کاملOn Commuting Matrix Differential Operators
If the differential expressions P and L are polynomials (over C) of another differential expression they will obviously commute. To have a P which does not arise in this way but satisfies [P,L] = 0 is rare. Yet the question of when it happens has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). In this paper the question is answered in the...
متن کاملEssentially Commuting Toeplitz Operators
For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...
متن کاملCommuting aggregation operators
We will investigate so-called commuting operators and their relationship to bisymmetry and domination. In the case of bisymmetric aggregation operators we will show a sufficient condition ensuring that two operators commute, while for bisymmetric aggregation operators with neutral element we will even give a full characterization of commuting n-ary operators by means of unary commuting operators.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1980
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-43-1-137-142