A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz ope...

We compute the norm of the restriction of a Schur multiplier, arising from a multiplication operator, to a coordinate subspace. This result is used to generalize Wielandt’s minimax inequality. Furthermore, we compute various s-numbers of an elementary Schur multiplier and determine criteria for membership of such multipliers in certain operator ideals.

We prove that the quadratic second quantization of an operator p on L2(Rd)∩L∞(Rd) is an orthogonal projection on the quadratic Fock space if and only if p = MχI , where MχI is a multiplication operator by a characteristic function χI .

Let S be the multiplication operator by an independent variable x in L2(0, 1) and V be an integral operator of Volterra type. We find conditions for T := S + V to be similar to S and discuss some generalisations of the results obtained to an abstract setting.

We show that b ∈ BMO( n) if and only if the commutator [b, Iα] of the multiplication operator by b and the fractional integral operator Iα is bounded from generalized Morrey spaces Lp,φ( n) to Lq,φ q/p ( n), where φ is non-decreasing, and 1 < p < ∞, 0 < α < n and 1/q = 1/p− α/n.

A class of enhancement techniques is proposed for images in arbitrary dimension D. They are free from either space/frequency (scale) or grey references. There are two subclasses. One subclass is the chain: {Negative Laplace operator, Multiplication by Power (γ−1) of modulus-Laplace value, Inverse Negative Laplace operator} together with generalized versions. The generalization of the Negative L...

We study a variant of the univariate approximate GCD problem, where the coefficients of one polynomial f(x)are known exactly, whereas the coefficients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]/(f). In particular, the structure of the null space of the multiplicat...

In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables can be derived as a specific case of suggested quantization if dynam...

The augmented Bergman complex of a closure operator on finite set interpolates between the order proper flats and independence operator. In 2020, Braden, Huh, Matherne, Proudfoot, Wang showed that complexes matroids are always gallery-connected, recently Bullock, Kelley, Reiner, Ren, Shemy, Shen, Sun, Tao, Zhang strengthened "gallery-connected" to "shellable" by providing two classes shelling o...