This paper considers the problem of approximating the spectral factor of continuous spectral densities with finite Dirichlet energy based on finitely many samples of these spectral densities. Although there exists a c...
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This paper considers the problem of approximating the spectral factor of continuous spectral densities with finite Dirichlet energy based on finitely many samples of these spectral densities. Although there exists a closed form expression for the spectral factor, this formula shows a very complicated behavior because of the non-linear dependency of the spectral factor from spectral density and because of a singular integral in this expression. Therefore approximation methods are usually applied to calculate the spectral factor. It is shown that there exists no sampling-based method which depends continuously on the samples and which is able to approximate the spectral factor for all densities in this set. Instead, to any sampling-based approximation method there exists a large set of spectral densities so that the approximation method does not converge to the spectral factor for every spectral density in this set as the number of available sampling points is increased. The paper will also show that the same results hold for sampling-based algorithms for the calculation of the outer function in the theory of Hardy spaces. (C) 2020 Elsevier Inc. All rights reserved.
The classical theorems of Mittag-Leffler and Weierstrass show that when (lambda(n))(n >= 1) is a sequence of distinct points in the open unit disk D, with no accumulation points in D, and (w(n))(n >= 1) is any s...
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The classical theorems of Mittag-Leffler and Weierstrass show that when (lambda(n))(n >= 1) is a sequence of distinct points in the open unit disk D, with no accumulation points in D, and (w(n))(n >= 1) is any sequence of complex numbers, there is an analytic function phi on D for which phi(lambda(n)) = w(n). A celebrated theorem of Carleson [2] characterizes when, for a bounded sequence (w(n))(n >= 1), this interpolating problem can be solved with a bounded analytic function. A theorem of Earl [5] goes further and shows that when Carleson's condition is satisfied, the interpolating function phi can be a constant multiple of a Blaschke product. Results from [4] determine when the interpolating function phi can be taken to be zero free. In this paper we explore when phi can be an outer function.
We relate the exponential integrability of the conjugate function (f) over tilde to the size of the gap in the essential range of f. Our main result complements a related theorem of Zygmund.
We relate the exponential integrability of the conjugate function (f) over tilde to the size of the gap in the essential range of f. Our main result complements a related theorem of Zygmund.
In this article, the authors introduce and study the performance of two novel parametric families of Nyquist intersymbol interference-free pulses. Using only two design parameters, the proposed pulses yield an enhance...
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In this article, the authors introduce and study the performance of two novel parametric families of Nyquist intersymbol interference-free pulses. Using only two design parameters, the proposed pulses yield an enhanced performance compared to the sophisticated flipped-inverse hyperbolic secant (asech) filter, which was recently documented in the literature. Although the construction of parametric families originates from the work of Beaulieu and Damen, the authors' approach is based on the concept of 'inner' and 'outer' functions and for this reason a higher flexibility in the choice of the family members is achieved. The proposed pulses may decay slower than the original raised-cosine (RC) pulse outside the pulse interval, but exhibit a more pronounced decrease in the amplitudes of the two largest sidelobes and this accounts for their improved robustness to error probabilities. It is clearly shown, via simulation results, that a lower bit error rate (BER), compared to the existing pulses, can be achieved for different values of the roll-off factor and timing jitter. Moreover, a smaller maximum distortion as well as a more open-eye diagram are attained which further demonstrate the superiority of the proposed pulse shaping filters.
We identify the functions whose polynomial multiples are weak* dense in Qp spaces and prove that if |f(z)|≥|g(z)| and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mz on Qp ...
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We identify the functions whose polynomial multiples are weak* dense in Qp spaces and prove that if |f(z)|≥|g(z)| and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mz on Qp spaces is cellular indecomposable.
We try to identify the functions whose poly. nomial multiples are dense in the logarithmic weighted VMOA space (VMOA(log)) and prove that if vertical bar f (z)vertical bar >= vertical bar g(z)vertical bar in the un...
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We try to identify the functions whose poly. nomial multiples are dense in the logarithmic weighted VMOA space (VMOA(log)) and prove that if vertical bar f (z)vertical bar >= vertical bar g(z)vertical bar in the unit disk and g is cyclic in VMOA(log), then f is cyclic.
We identify the functions whose polynomial multiples are weak＊ dense in Qp spaces and prove that if ｜f（z）｜ ≥ ｜g（z）｜ and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operato...
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We identify the functions whose polynomial multiples are weak＊ dense in Qp spaces and prove that if ｜f（z）｜ ≥ ｜g（z）｜ and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mx on Qp spaces is cellular indecomposable.
In general, better performance can be achieved with a controlled minimum-phase system than a controlled non-minimum-phase system. We show that a wide class of second-order infinite-dimensional systems with either velo...
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In general, better performance can be achieved with a controlled minimum-phase system than a controlled non-minimum-phase system. We show that a wide class of second-order infinite-dimensional systems with either velocity or position measurements are minimum-phase. The results are illustrated by two examples.
Let D denote the open unit disk and letbe analytic on D with positive monotone decreasing coefficientsfn. We answer several questions posed by J. Cima on the location of the zeros of polynomial approximates which he o...
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Let D denote the open unit disk and letbe analytic on D with positive monotone decreasing coefficientsfn. We answer several questions posed by J. Cima on the location of the zeros of polynomial approximates which he originally posed about outer functions. In particular, we show that the zeros of Cesàro approximants tofare well-behaved in the following sense: (1) ifthen γD is the only accumulation set for the zeros of the Cesàro sums off; and (2) iffhas a representationwherethen we give sufficient conditions so that the convex hull of the zeros of the Cesàro sums offwill contain D.
Using the Stone-Cech compactification beta Z of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy sp...
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Using the Stone-Cech compactification beta Z of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy spaces H-p(mu), 1 less than or equal to p less than or equal to infinity, the corresponding subspaces H-0(p)(mu) are all singly generated. This shows the existence of maximal weak-* Dirichlet algebras, different from H-infinity of the disc, for which the single generator problem is settled.
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