Quasi-Herglotz functions and convex optimization

• We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modeling 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 modeling perspectives of Herglotz functions 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 modeling of a non-passive gain media formulated as a convex optimization problem,where the generating measure is modeled by using a finite expansion of B-splines and point masses.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Annan elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Other Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

Nyckelord

Quasi-Herglotz functions

non-passive systems

approximation

convex optimization

sum rules

Mathematics

matematik

Waves and Signals

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vet (ämneskategori)

rap (ämneskategori)