This paper discusses several structural and fundamental properties of the $k^{th}$-order slant Toeplitz operators on Lebesgue space $n$- torus $\mathbb{T}^n$, for integers $k\geq 2$ $n\geq 1$. We obtain certain equivalent conditions commutativity essential these operators. In last section, we deal with spectrum a operator $L^2(\mathbb{T}^n)$ investigate such an to be isometry, hyponormal or nor...

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

This paper discusses balanced realization and model order reduction for both continuoustime and discrete-time general nonlinear systems based on singular value analysis of the corresponding Hankel operators. Singular value analysis clarifies the gain structure of a given nonlinear operator. Here it is proved that singular value analysis of smooth Hankel operators defined on Hilbert spaces can b...

This letter considers how to approximately reconstruct a cascade system from a given unstructured system estimate. Many system identification methods, including subspace methods, provide reliable but generally unstructured black-box models. The problem we consider is how to find cascade systems that are close to such black-box models. For this, we use model matching techniques and optimal weigh...