222 citations · 550 across the 18 of their papers we have counts for
18 papers
Weak -frames and weak -semi-frames
Jean-Pierre Antoine, Giorgia Bellomonte, Camillo Trapani
After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator or, for short, a \emph{…
Lower semi-frames and metric operators
J-P. Antoine, R. Corso, C. Trapani
This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-a…
Reproducing pairs of measurable functions and partial inner product spaces
Jean-Pierre Antoine, Camillo Trapani
We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable…
Operator (quasi-)similarity, quasi-Hermitian operators and all that
Jean-Pierre Antoine, Camillo Trapani
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we…
Reproducing pairs of measurable functions
Jean-Pierre Antoine, Michael Speckbacher, Camillo Trapani
We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates t…
Metric operators, generalized hermiticity and lattices of Hilbert lpaces
Jean-Pierre Antoine, Camillo Trapani
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric…
Operators on Partial Inner Product Spaces: Towards a Spectral Analysis
Jean-Pierre Antoine, Camillo Trapani
Given a LHS (Lattice of Hilbert spaces) and a symmetric operator in , in the sense of partial inner product spaces, we define a generalized resolvent for and stu…
Some remarks on quasi-Hermitian operators
Jean-Pierre Antoine, Camillo Trapani
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric…
Partial inner product spaces, metric operators and generalized hermiticity
Jean-Pierre Antoine, Camillo Trapani
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operat…
A spatio-temporal Gaussian-Conical wavelet with high aperture selectivity for motion and speed analysis
Patrice Brault, Jean-Pierre Antoine
The construction of a spatio-temporal wavelet and its tuning to speed was first realized in the 90s on the Morlet wavelet by M. Duval-Destin \cite{Duval-Destin91a,Duval-Destin92}.…
Bounded elements in certain topological partial *-algebras
Jean-Pierre Antoine, Camillo Trapani, Francesco Tschinke
We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras…
Frames, semi-frames, and Hilbert scales
J-P. Antoine, P. Balazs
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame…
Frames and Semi-Frames
Jean-Pierre Antoine, Peter Balazs
Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (…
Classification of General Sequences by Frame-Related Operators
Peter Balazs, Diana T. Stoeva, Jean-Pierre Antoine
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well…
Topological partial *-algebras: Basic properties and examples
J. -P. Antoine, F. Bagarello, C. Trapani
Let be a partial *-algebra endowed with a topology that makes it into a locally convex topological vector space . Then is called a topological partial *-algebra i…
Extension of representations in quasi *-algebras
J. -P. Antoine, F. Bagarello, C. Trapani
Let be a topological quasi *-algebra, which means in particular that is a topological *-algebra, dense in . Let be a *-representation of in some pre…
Weighted and controlled frames
Peter Balazs, Jean-Pierre Antoine, Anna Grybos
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop…
Temporally stable coherent states for infinite well and Pöschl-Teller potentials
J-P. Antoine, J-P. Gazeau, P. Monceau +2
This paper is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trappe…