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Extensions of Bessel sequences to dual pairs of frames
Christensen, O.,Kim, H.O.,Kim, R.Y. Academic Press 2013 Applied and computational harmonic analysis Vol.34 No.2
Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair of dual frames. If the given Bessel sequences are Gabor systems in L<SUP>2</SUP>®, the extension can be chosen to have Gabor structure as well. We also show that if the generators of the given Gabor Bessel sequences are compactly supported, we can choose the generators of the added Gabor systems to be compactly supported as well. This is a significant improvement compared to the extension of a Bessel sequence to a tight frame, where the added generator only can be compactly supported in some special cases. We also analyze the wavelet case, and find sufficient conditions under which a pair of wavelet systems can be extended to a pair of dual frames.
International Repercussions of Source-based Capital Income Taxation
Christensen, Thomas Alslev,Nielsen, Søren Bo 세종대학교 국제경제연구소 1995 Journal of Economic Integration Vol.10 No.1
The paper is concerned with international effects of source-based capital income taxation in a large economy. We derive, within the context of a twocountry overlapping generations model in continuous time, the implications of such taxation for the world interest rate and for investment, consumption, saving and external balances at home and abroad. Furthermore, we argue that higher source-based taxes will hurt foreigners alive at the time of the policy change, whereas future citizens abroad stand to benefit. Finally, the effects of source-and residence-based taxed are compared.
On Gabor frames generated by sign-changing windows and B-splines
Christensen, O.,Kim, H.O.,Kim, R.Y. Academic Press 2015 Applied and computational harmonic analysis Vol.39 No.3
For a class of compactly supported windows we characterize the frame property for a Gabor system {E<SUB>mb</SUB>T<SUB>na</SUB>g}<SUB>m,n@?Z</SUB>, for translation parameters a belonging to a certain range depending on the support size. We show that the obstructions to the frame property are located on a countable number of ''curves.'' For functions that are positive on the interior of the support these obstructions do not appear, and the considered region in the (a,b) plane is fully contained in the frame set. In particular this confirms a recent conjecture about B-splines by Grochenig in that particular region. We prove that the full conjecture is true if it can be proved in a certain ''hyperbolic strip.''
On entire functions restricted to intervals, partition of unities, and dual Gabor frames
Christensen, O.,Kim, H.O.,Kim, R.Y. Academic Press 2015 Applied and computational harmonic analysis Vol.38 No.1
Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire functions that lead to a partition of unity in this way, and we provide characterizations of the ''cut-off'' entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity. Applied to Gabor analysis this leads to constructions of dual pairs of Gabor frames with low redundancy, generated by trigonometric polynomials with small support and desired regularity.