| 1. |
- Ivanenko, Yevhen, et al.
(author)
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Quasi-Herglotz functions and convex optimization
- 2020
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In: Royal Society Open Science. - : The Royal Society Publishing. - 2054-5703. ; 7:1, s. 1-15
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Journal article (peer-reviewed)abstract
- We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.
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| 2. |
- Laksman, Efraim, et al.
(author)
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Generalized upper bounds on the minimum distance of PSK block codes
- 2015
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In: IMA Journal of Mathematical Control and Information. - : Oxford Journals. - 0265-0754 .- 1471-6887. ; 32:2, s. 305-327
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Research review (peer-reviewed)abstract
- This paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase shift keying (PSK) block codes, that are explicit in three parameters: alphabet size, block length and code size. The bounds are primarily generalized from codes over symmetric PSK to codes over asymmetric PSK and also to general alphabet size. Furthermore, block codes are optimized in the presence of other types of noise than Gaussian, which induces also non-Euclidean distance measures. In some instances, codes over asymmetric PSK prove to give higher Euclidean distance than any code over symmetric PSK with the same parameters. We also provide certain classes of codes that are optimal among codes over symmetric PSK.
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| 3. |
- Nedic, Mitja, et al.
(author)
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Herglotz functions and applications in electromagnetics
- 2020
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In: Advances in Mathematical Methods for Electromagnetics. - : Institution of Engineering and Technology. - 9781785613845 - 9781785613852 ; , s. 491-514
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Book chapter (other academic/artistic)abstract
- Herglotz functions inevitably appear in pure mathematics, mathematical physics, and engineering with a wide range of applications. In particular, they are the pertinent functions to model passive systems, and thus appear in modeling of electromagnetic phenomena in circuits, antennas, materials, and scattering. In this chapter, we review the basic theory of Herglotz functions and its applications to determine sum rules and physical bounds for passive systems.
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| 5. |
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| 6. |
- Engström, Christian, et al.
(author)
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Spectral properties of a class of operator functions with applications to the Moore-Gibson-Thompson equation with memory
- 2024
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In: Journal of Mathematical Analysis and Applications. - : Elsevier. - 0022-247X .- 1096-0813. ; 532:2
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Journal article (peer-reviewed)abstract
- In this study, we present spectral enclosures and accumulation of eigenvalues of a class of operator functions with several unbounded operator coefficients. Our findings have direct relevance to the third-order Moore-Gibson-Thompson equation with memory and additional damping. The new results include sufficient conditions for the accumulation of branches of eigenvalues to the essential spectrum and new spectral enclosures for operator functions with several unbounded operator coefficients. To illustrate the analytical results, we apply the abstract findings to concrete equations of the Moore-Gibson-Thompson type. Additionally, we employ numerical computations to further elucidate the analytical results.
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| 7. |
- Holst, Anders, et al.
(author)
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Weyl product algebras and modulation spaces
- 2007
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In: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236. ; 251:2, s. 463-491
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Journal article (peer-reviewed)abstract
- We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions omega we prove that M-(omega)(p,q) is an algebra under the Weyl product if p epsilon [1, infinity] and 1 <= q <= min(p, p '). For the remaining cases P epsilon [1, infinity] and min(p, p ') < q <= infinity we show that the unweighted spaces M-p,M-q are not algebras under the Weyl product. (C) 2007 Elsevier Inc. All rights reserved.
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| 8. |
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| 9. |
- Ibragimov, Nail H., et al.
(author)
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Utilization of photon orbital angular momentum in the low-frequency radio domain
- 2007
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In: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 99:8
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Journal article (peer-reviewed)abstract
- We show numerically that vector antenna arrays can generate radio beams that exhibit spin and orbital angular momentum characteristics similar to those of helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (1 GHz), digital techniques can be used to coherently measure the instantaneous, local field vectors and to manipulate them in software. This enables new types of experiments that go beyond what is possible in optics. It allows information-rich radio astronomy and paves the way for novel wireless communication concepts.
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| 10. |
- Ivanenko, Yevhen, et al.
(author)
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Passive Approximation and Optimization Using B-Splines
- 2019
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In: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 79:1, s. 436-458
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Journal article (peer-reviewed)abstract
- A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.
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