Noncommutative Function-Theoretic Operator Theory and Applications

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

The Spectrum of Mapping Ideals of Type Variable Exponent Function Space of Complex Variables with Some Applications

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.

Simulation of ship handling in reverse

One of the main problems of seamanship is steering the boat in reverse modes. This skill can be achieved using simulators or simulators that work based on a mathematical model. This model should adequately describe all ship maneuvers, including simulation in reverse modes. The article deals with the mathematical modeling of maneuvering from a ship in reverse. The authors performed model calculations, basic test maneuvers, such as “Circulation”, “Exit Circulation” and “Zigzag”. The analysis of trajectories testifies to the qualitative correspondence of the calculation results according to the mathematical model to the practice of navigation, and this model can be used for automatic control of the vessel, for assessing the movement of the vessel in reverse, and teaching navigation skills on simulators and simulators. The vessel when moving in reverse, at low speeds obeys the steering organ, but at speeds greater than the average stroke on the backward shift, it leaves the circulation very slowly and sometimes becomes uncontrollable. The withdrawal of a reverse circulation vessel is extremely difficult and requires additional skills and abilities from the navigator.

Trends in the Airglow Temperatures in the MLT Region—Part 2: SABER Observations and Comparisons to Model Simulations

The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature measurements at low latitudes from 89 km to 97 km were used to derive the F10.7 and Ap index trends, and the trends were compared to model simulations. The annual mean nonzonal (e.g., at the model simulation location at 18° N, 290° E) SABER temperature showed a good-to-moderate correlation with F10.7, with a trend of 4.5–5.3 K/100 SFU, and a moderate-to-weak correlation with the Ap index, with a trend of 0.1–0.3 K/nT. The annual mean zonal mean SABER temperature was found to be highly correlated with the F10.7, with a similar trend, and moderately correlated with the Ap index, with a trend in a similar range. The correlation with the Ap index was significantly improved with a slightly larger trend when the zonal mean temperature was fitted with a 1-year backward shift in the Ap index. The F10.7 (Ap index) trends in the simulated O2 and the O(1S) temperature were smaller (larger) than those in the annual mean nonzonal mean SABER temperature. The trends from the simulations were better compared to those in the annual mean zonal mean temperature. The comparisons were even better when compared to the trend results obtained from fitting with a backward shift in the Ap index.

Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces

We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces ${\mathcal{F}}_W^p$, whose weight is not necessarily radial. We show that in the spaces ${\mathcal{F}}_W^p$, which contain the polynomials as a dense subspace (in particular, in the radial case), all nontrivial backward shift invariant subspaces are of the form $\mathcal{P}_n$, that is, finite-dimensional subspaces consisting of polynomials of degree at most $n$. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type), we establish an analogue of de Branges’ ordering theorem. We then construct examples that show that the result fails for general Fock-type spaces of larger growth.