Construction, Extension and Coupling of Frames on Finite Dimensional Pontryagin Space

2014/08/27 by German Escobar, Germán Escobar, Kevin Esmeral +4
Engineering · Mathematics · #46C20 #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary 42C15 #Secondary 47B50 #math.FA #msc:42C15 #msc:46C20 #msc:47B50

paper · pdf · doi:10.48550/arxiv.1408.6584

arxiv created 2014/08/27 · openalex publication_date 2014/08/27 · arxiv updated 2014/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we extend to finite-dimensional Pontryagin spaces the methods used in \citeCasazzaLeon,Deguang to build frames from an adjoint and positive operator. It is proved that any frame in finite dimensional Pontryagin space K is J-orthogonal projection of a frame for a space H such that K\subsetH. Furthermore, given \k_n\_n=1^m and \x_n\_n=1^k frames for K and H respectively, we build a finite-dimensional Pontryagin space \mathfrakK and a frame \y_n\_n=1^N for \mathfrakK such that K,H⊂\mathfrakK and \k_n\_n=1^m,\x_n\_n=1^k⊂ \y_n\_n=1^N.

Citations

• On a family of frames for Krein spaces
• The wavelet transform, time-frequency localization and signal analysis

Related

• Frames for subspaces of ℂ^N
• Duality for Frames in Krein Spaces
• On J-frames related to maximal definite subspaces
• A brief introduction to Hilbert space frame theory and its applications
• K-b-frames for Hilbert spaces and the b-adjoint operator