New York Journal of Mathematics Invariance under bounded
... The results carried in this article stem from the famous and fundamental theorem of Beurling, [4], related to the characterization of the invariant subspaces of the operator of multiplication by the coordinate function z — also known as the shift operator — on the classical Hardy space H 2 of the op ...
... The results carried in this article stem from the famous and fundamental theorem of Beurling, [4], related to the characterization of the invariant subspaces of the operator of multiplication by the coordinate function z — also known as the shift operator — on the classical Hardy space H 2 of the op ...
THE DYNAMICAL MORDELL-LANG PROBLEM FOR NOETHERIAN SPACES
... where the lim sup is taken over intervals I in the natural numbers. We say that a subset S of the natural numbers has Banach density zero if δ(S) = 0. Definition 1.3. Let X be a topological space. We say that X is Noetherian if it satisfies the descending chain condition for its closed subsets, i.e. ...
... where the lim sup is taken over intervals I in the natural numbers. We say that a subset S of the natural numbers has Banach density zero if δ(S) = 0. Definition 1.3. Let X be a topological space. We say that X is Noetherian if it satisfies the descending chain condition for its closed subsets, i.e. ...
finitegroups.pdf
... he defines its rank to be its dimension as a vector space. The reason these posets are interesting is that G acts on them in such a way that their topological properties relate nicely to algebraic properties of G. The action of G is by conjugation. If H is a subgroup of G and g ∈ G, write H g = gHg ...
... he defines its rank to be its dimension as a vector space. The reason these posets are interesting is that G acts on them in such a way that their topological properties relate nicely to algebraic properties of G. The action of G is by conjugation. If H is a subgroup of G and g ∈ G, write H g = gHg ...
3. Stieltjes-Lebesgue Measure
... map. There exists a unique measure μ : B(R) → [0, +∞] such that: ∀a, b ∈ R , a ≤ b , μ(]a, b]) = F (b) − F (a) Definition 20 Let F : R → R be a right-continuous, non-decreasing map. We call Stieltjes measure on R associated with F , the unique measure on B(R), denoted dF , such that: ∀a, b ∈ R , a ≤ ...
... map. There exists a unique measure μ : B(R) → [0, +∞] such that: ∀a, b ∈ R , a ≤ b , μ(]a, b]) = F (b) − F (a) Definition 20 Let F : R → R be a right-continuous, non-decreasing map. We call Stieltjes measure on R associated with F , the unique measure on B(R), denoted dF , such that: ∀a, b ∈ R , a ≤ ...
Complex vectors
... co-polarized component of E with respect to h contributes to the value of p(h, E) and complete polarization match p(h, E) = 1 is obtained for h x E* = 0, or when h and E* are parallel vectors. On the other hand, there is a total mismatch /?(h,E) = 0 for perpendicular vectors h, E, or when the incomi ...
... co-polarized component of E with respect to h contributes to the value of p(h, E) and complete polarization match p(h, E) = 1 is obtained for h x E* = 0, or when h and E* are parallel vectors. On the other hand, there is a total mismatch /?(h,E) = 0 for perpendicular vectors h, E, or when the incomi ...
Continuous cohomology of groups and classifying spaces
... H° and Hx behave entirely as expected, but for H2 life becomes more interesting. Abstract group extensions are always split as sets, in contrast to the topological case. Hu in 1951 [31] (and independently Heller) showed that H?(G; A) classified topologically split group extensions, i.e. short exact ...
... H° and Hx behave entirely as expected, but for H2 life becomes more interesting. Abstract group extensions are always split as sets, in contrast to the topological case. Hu in 1951 [31] (and independently Heller) showed that H?(G; A) classified topologically split group extensions, i.e. short exact ...
Some applications of the ultrafilter topology on spaces of valuation
... When A is the prime subring of K, we will simply denote by Zar(K) the space Zar(K|A). Recall that O. Zariski in [16] introduced a topological structure on the set Z := Zar(K|A) by taking, as a basis for the open sets, the subsets BF := {V ∈ Z | V ⊇ F }, for F varying in the family of all finite subs ...
... When A is the prime subring of K, we will simply denote by Zar(K) the space Zar(K|A). Recall that O. Zariski in [16] introduced a topological structure on the set Z := Zar(K|A) by taking, as a basis for the open sets, the subsets BF := {V ∈ Z | V ⊇ F }, for F varying in the family of all finite subs ...