58 research outputs found
-g-frames in tensor products of hilbert -modules
In this paper, we study -g-frames in tensor products of Hilbert
-modules. We show that a tensor product of two -g-frames is a
-g-frames, and we get some result
Independence, infinite dimension, and operators
In [Applied and Computational Harmonic Analysis, 46(3), 664-673, 2019] O.
Christensen and M. Hasannasab observed that assuming the existence of an
operator sending to for all (where
is a sequence of vectors) guarantees that is linearly independent if and only if . In this article, we recover this result as a particular
case of a general order-theory-based model-theoretic result. We then return to
the context of vector spaces to show that, if we want to use a condition like
for all where is countable as a replacement
of the previous one, the conclusion will only stay true if is
conjugate to the successor function defined on
. We finally prove a tentative generalization of the result, where
we replace the condition for all where is
conjugate to the successor function with a more sophisticated one, and to which
we have not managed to find a new application yet.Comment: 12 page
Functions with a maximal number of finite invariant or internally-1-quasi-invariant sets or supersets
A relaxation of the notion of invariant set, known as -quasi-invariant
set, has appeared several times in the literature in relation to group
dynamics. The results obtained in this context depend on the fact that the
dynamic is generated by a group. In our work, we consider the notions of
invariant and 1-internally-quasi-invariant sets as applied to an action of a
function on a set . We answer several questions of the following type,
where : what are the functions for which every finite subset
of is internally--quasi-invariant? More restrictively, if , what are the functions for which every finite interval of
is internally--quasi-invariant? Last, what are the functions for which
every finite subset of admits a finite internally--quasi-invariant
superset? This parallels a similar investigation undertaken by C. E. Praeger in
the context of group actions.Comment: 27 page
Solution of a functional equation on compact groups using Fourier analysis
Let be a compact group, let be a fixed element and let be a continuous automorphism on such that . Using the non-abelian Fourier transform, we determine the non-zero continuous solutions of the functional equation in terms of unitary characters of
--frames for Hilbert spaces and the -adjoint operator
In this paper, we will generelize -frames; a new concept of frames for
Hilbert spaces, by --frames. The idea is to take a sequence from a Banach
space and see how it can be a frame for a Hilbert space. Instead of the scalar
product we will use a new product called the -dual product and it is
constructed via a bilinear mapping. We will introduce new results about this
product, about -frames, and about --frames, and we will also give some
examples of both -frames and --frames that have never been given
before. We will give the expression of the reconstruction formula of the
elements of the Hilbert space. We will as well study the stability and
preservation of both -frames and --frames; and to do so, we will give
the equivalent of the adjoint operator according to the -dual product
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