Electromagnetic Fields – Restrictions and Approximation

Computational aspects of constructing the approximating Herglotz functions in inverse scattering problems

“…The body reconstruction problem considered here is formulated in [1]. Here we directly proceed to the method description.…”

“…A method of body shape reconstruction at its resonant frequencies was proposed in [1] and developed in [2][3][4]. The method uses the property that any set of scattering patterns can be noncomplete at these frequencies.…”

“…From the other hand, we can carry out numerical calculations only in certain finite-dimensional spaces and find the Herglotz function also in a finite-dimensional spaces. The question is whether the sequence of Herglotz functions obtained in the algorithm described in [1] possesses the approximate property for the eigenfunction, in particular, when the exact Herglotz functions does not exist. Having analyzed the numerical results obtained by applying the method to reconstruction of bodies with different shapes, we are likely at the point to answer this question positively and say that the method can be a powerful tool for solving inverse scattering problems at the resonant frequencies.…”

Prof. Boris Z. Katsenelenbaum – Mastermind, Organizer, and Contributor to the DIPED Seminar/Workshop

“…The main contribution and results related to the first area were summarized in book [9]. The subject of this book falls within the scope of three disciplines, namely the antenna theory, highfrequency electrodynamics and mathematical physics.…”

Synthesis of Antenna Systems According to the Desired Amplitude Radiation Characteristics

“…One can turn out that its solutions represent the unreliazable patterns [20]. In order to avoid such solutions, it is necessary to substitute formula (26) into (42) instead of f .…”