Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...

In my (DNA) dreams: A tri-G-quadruplex was constructed from three strands (T1-T3) of DNA using duplex formation to guide the G-rich tracts into close proximity with the addition of Li(+) ions (see scheme). The defined G-quadruplex structure was formed upon addition of Na(+) ions and characterized by gel electrophoresis and spectroscopy.

Frames have applications in numerous fields of mathematics and engineering. The fundamental property of frames which makes them so useful is their overcompleteness. In most applications, it is this overcompleteness that is exploited to yield a decomposition that is more stable, more robust, or more compact than is possible using nonredundant systems. This work presents a quantitative framework ...

The quantum mechanical harmonic oscillator Hamiltonian H = (t − ∂ t )/2 generates a one–parameter unitary group W (θ) = e in L(R) which rotates the time–frequency plane. In particular, W (π/2) is the Fourier transform. When W (θ) is applied to any frame of Gabor wavelets, the result is another such frame with identical frame bounds. Thus each Gabor frame gives rise to a one–parameter family of ...