We consider frames in a finite-dimensional Hilbert space H n where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R 2 was previously defined using polar coordinates and was used to characterize tight frames in R 2 in a geometric fashion. Reformulating the definition of a diagram vector in R 2 we provide a natural… (More)
The purposes of this study were to evaluate the asymmetry of the sphenoid bone and to determine its suitability as a reference for analyzing asymmetry of the skull. Thirty-seven dry skulls from India were divided into group A (n = 18), with a right-left length discrepancy of less than 2 mm for both the external acoustic meatus-frontozygomatic suture and… (More)
Title of Doctoral Dissertation " Exponential box splines and other types of non-polynomial B-splines " .
In this paper, we characterize the space of almost periodic (AP) functions in one variable using either a Weyl-Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively, affine) system is an L 2 (IR)-frame. Moreover, the frame bounds of the system… (More)