479 research outputs found
Trace ideals for Fourier integral operators with non-smooth symbols II
We consider Fourier integral operators with symbols in modulation spaces and
non-smooth phase functions whose second orders of derivatives belong to certain
types of modulation space. We establish continuity and Schatten-von Neumann
properties of such operators when acting on modulation spaces.Comment: 25 page
A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators
This chapter offers a detailed survey on intrinsically localized frames and
the corresponding matrix representation of operators. We re-investigate the
properties of localized frames and the associated Banach spaces in full detail.
We investigate the representation of operators using localized frames in a
Galerkin-type scheme. We show how the boundedness and the invertibility of
matrices and operators are linked and give some sufficient and necessary
conditions for the boundedness of operators between the associated Banach
spaces.Comment: 32 page
Constructions of regular algebras
Criterion of (Shilov) regularity for weighted algebras on a
locally compact abelian group is known by works of Beurling (1949) and
Domar (1956). In the present paper this criterion is extended to translation
invariant weighted algebras with . Regular algebras
are constructed on any sigma-compact abelian group . It was proved earlier
by the author that sigma-compactness is necessary (in the abelian case) for the
existence of weighted algebras with .Comment: Submitted to Mat. Sborni
A luciferase-based quick potency assay to predict chondrogenic differentiation.
Chondrogenic differentiation of adipose derived stem cells (ASC) is challenging but highly promising for cartilage repair. Large donor variability of chondrogenic differentiation potential raises the risk for transplantation of cells with reduced efficacy and a low chondrogenic potential. Therefore quick potency assays are required in order to control the potency of the isolated cells before cell transplantation. Current in vitro methods to analyze the differentiation potential are time consuming and thus, a novel enhancer and tissue-specific promoter combination was employed for the detection of chondrogenic differentiation of ASC in a novel quick potency bioassay. Human primary ASC were co-transfected with the Metridia luciferase based collagen type II reporter gene pCMVE_ACDCII-MetLuc together with a Renilla control plasmid and analyzed for their chondrogenic potential. On day 3 after chondrogenic induction, the luciferase activity was induced in all tested donors under three dimensional (3D) culture conditions and in a second approach also under 2D culture conditions. With our newly developed quick potency bioassay we can determine chondrogenic potential already after 3 days of chondrogenic induction and under 2D culture conditions. This will enhance the efficiency of testing cell functionality, which should allow in the future to predict the suitability of cells derived from individual patients for cell therapies, in a very short time and at low costs
Ultrasound-responsive gene-activated matrices (GAMs) for osteogenic gene therapy using matrix-assisted sonoporation (MAS)
Technological Progress, Employment and the Lifetime of Capital
We study the impact of technological progress on the level of employment in a vintage capital model where: i) capital and labor are gross complementary; ii) labor supply is endogenous and indivisible; iii) there is full employment, and iv) the rate of labor-saving technological progress is endogenous. We characterize the stationary distributions of vintage capital goods and the corresponding equilibrium values for employment and capital lifetime. It is shown that both variables are non-monotonic functions of technological progress indicators. Technological accelerations are found to increase employment provided innovations are not too radical
On the probabilistic Cauchy theory for nonlinear dispersive PDEs
In this note, we review some of the recent developments in the well-posedness
theory of nonlinear dispersive partial differential equations with random
initial data.Comment: 26 pages. To appear in Landscapes of Time-Frequency Analysis, Appl.
Numer. Harmon. Ana
A new ketogenic formulation improves functional outcome and reduces tissue loss following traumatic brain injury in adult mice
Cornerstones of Sampling of Operator Theory
This paper reviews some results on the identifiability of classes of
operators whose Kohn-Nirenberg symbols are band-limited (called band-limited
operators), which we refer to as sampling of operators. We trace the motivation
and history of the subject back to the original work of the third-named author
in the late 1950s and early 1960s, and to the innovations in spread-spectrum
communications that preceded that work. We give a brief overview of the NOMAC
(Noise Modulation and Correlation) and Rake receivers, which were early
implementations of spread-spectrum multi-path wireless communication systems.
We examine in detail the original proof of the third-named author
characterizing identifiability of channels in terms of the maximum time and
Doppler spread of the channel, and do the same for the subsequent
generalization of that work by Bello.
The mathematical limitations inherent in the proofs of Bello and the third
author are removed by using mathematical tools unavailable at the time. We
survey more recent advances in sampling of operators and discuss the
implications of the use of periodically-weighted delta-trains as identifiers
for operator classes that satisfy Bello's criterion for identifiability,
leading to new insights into the theory of finite-dimensional Gabor systems. We
present novel results on operator sampling in higher dimensions, and review
implications and generalizations of the results to stochastic operators, MIMO
systems, and operators with unknown spreading domains
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