Related papers: The Composite Operator Method (COM)
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
We develop an encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference from observational data called generalized optimal matching (GOM). The framework is given by generalizing a new…
We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…
An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results…
Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
The SOM algorithm is very astonishing. On the one hand, it is very simple to write down and to simulate, its practical properties are clear and easy to observe. But, on the other hand, its theoretical properties still remain without proof…
A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…
Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we consider a restricted additive method for the Poisson equation and write a…
Starting with the first-order singular Lagrangian, the canonical structure in the noncommutative quantum mechanics with the noncommutativities both of coordinates and momenta is investgated. Using the projection operator method (POM) for…
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.
Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition $S+T=\makeset{m+n}{m \in S, \: n \in T}$ and…