Related papers: Irregular and multi--channel sampling of operators
The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the…
In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
Periodic nonuniform sampling has been considered in literature as an effective approach to reduce the sampling rate far below the Nyquist rate for sparse spectrum multiband signals. In the presence of non-ideality the sampling parameters…
In this paper we show variant of the spectral theorem using an algebraic Jordan-Schwinger map. The advantage of this approach is that we don't have restriction of normality on the class of operators we consider. On the other side, we have…
Time and band limiting operators are expressed as functions of the confluent Heun operator arising in the spheroidal wave equation. Explicit formulas are obtained when the bandwidth parameter is either small or large and results on the…
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…
The concept of translation of an operator allows to consider the analogous of shift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the…
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…
In this paper, we mainly investigate the nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain. We show that the nonuniform sampling for a random signal bandlimited in the LCT domain is…
Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and proposes solutions to a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations?…
Approximation properties of multivariate Kantorovich-Kotelnikov type operators generated by different band-limited functions are studied. In particular, a wide class of functions with discontinuous Fourier transform is considered. The…
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…
Using an abstract notion of semiclassical quantization for self-adjoint operators, we prove that the joint spectrum of a collection of commuting semiclassical self-adjoint operators converges to the classical spectrum given by the joint…
It is widely believed that statistical interpretation of quantum mechanics requires that density operators representing quantum states be normalized. We present a description of selective measurements in terms of density operators. The…
We consider random linear continuous operators $\Omega \to \mathcal{L}(\mathcal{H}, \mathcal{H})$ on a Hilbert space $\mathcal{H}$. For example, such random operators may be random quantum channels. The Central Limit Theorem is known for…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…
In this paper, we introduce a Stancu-type generalization of multivariate neural network operators by incorporating two parameters that perturb the sampling nodes. The proposed operators extend the existing neural network operator by…
In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…