Related papers: On Generalized Numerical Ranges of Quadratic Opera…
Oscillatory integral operators with $1$-homogeneous phase functions satisfying a convexity condition are considered. For these we show the $L^p - L^p$-estimates for the Fourier extension operator of the cone due to Ou--Wang via polynomial…
We prove that strictly elliptic operators with generalized Wentzell boundary conditions generate analytic semigroups of angle $\frac{\pi}{2}$ on the space of continuous function on a compact manifold with boundary.
In the recent paper by Mark C. Ho (2014) the notion of a $\lambda$-Toeplitz operator on the Hardy space $H^2(\mathbb{T})$ over the one-dimensional torus $\mathbb{T}$ was introduced and it was shown (under the supplementary condition) that…
We investigate the Cauchy problem for elliptic operators with $C^\infty$-coefficients at a regular set $\Omega \subset R^2$, which is a classical example of an ill-posed problem. The Cauchy data are given at the subset $\Gamma \subset…
We present a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In its standard form, the quantum volume operator is constructed from tetrahedra whose faces are endowed with…
If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on…
The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted…
The aim of this paper is to get the boundedness of rough sublinear operators generated by fractional integral operators on vanishing generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the…
This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…
We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in some algebras of smooth functions on the interval.
In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the…
Conditions are established for rank three partial isometries to have circular components contained in their Kippenhahn curves. In particular, such matrices with circular numerical ranges are described. It is also established that the…
A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…
We establish optimal $C^s$ boundary regularity for the most general class of (linear and translation invariant) nonlocal elliptic operator of order $2s$. Namely, we consider L\'evy operators that are symmetric and its Fourier symbol…
The notion of quasi-elliptic rings appeared as a result of an attempt to classify a wide class of commutative rings of operators found in the theory of integrable systems, such as rings of commuting differential, difference,…
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve if one imposes appropriate boundary conditions. Algebraic curves of the type thus obtained appear as irreducible components of…
Schur-Horn theorems focus on determining the diagonal sequences obtainable for an operator under all possible basis changes, formally described as the range of the canonical conditional expectation of its unitary orbit. Following a brief…
We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for…
Let $T$ be a bounded linear operator on a complex Hilbert space $\mathscr{H}.$ We obtain various lower and upper bounds for the numerical radius of $T$ by developing the Euclidean operator radius bounds of a pair of operators, which are…