Related papers: On Generalized Numerical Ranges of Quadratic Opera…

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a…

In this paper, we consider the higher Br\'ezin--Gross--Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac--Schwarz operators, quantum spectral curves, and $W^{(3)}$-constraints. For…

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on…

We present a formula for the norm of an elementary operator on a C*-algebra that seems to be new. The formula involves (matrix) numerical ranges and a kind of geometrical mean for positive matrices, the tracial geometric mean, which seems…

We study the pseudospectrum of a class of non-selfadjoint differential operators. Our work consists in a detailed study of the microlocal properties, which rule the spectral stability or instability phenomena appearing under small…

We introduce concepts of essential numerical range for the linear operator pencil $\lambda\mapsto A-\lambda B$. In contrast to the operator essential numerical range, the pencil essential numerical ranges are, in general, neither convex nor…

We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special…

In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted…

In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study…

We generalize several inequalities involving powers of the numerical radius for off-diagonal part of $2\times2$ operator matrices of the form $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, where $B, C$ are two operators. In…

In this article, we introduce a class of multilinear strongly singular integral operators with generalized kernels on the RD-space. The boundedness of these operators on weighted Lebesgue spaces is established. Moreover, two types of…

Let $({\cal X},\mu)$ be a measure space. For any measurable set $Y\subset{\cal X}$ let $1_Y : {\cal X}\to{\mathbb R}$ be the indicator of $Y$ and let $\pi_Y$ be the orthogonal projector $L^2({\cal X})\ni f\mapsto\pi_Y f = 1_Y f$. For any…

We give a refined Young inequality which generalizes the inequality by Zou--Jiang. We also show the upper bound for the logarithmic mean by the use of the weighted geometric mean and the weighted arithmetic mean. Furthermore, we show some…

Several new verifiable conditions are established for block matrices with scalar diagonal blocks to have the numerical range equal the convex hull of at most k ellipses where k by k is the size of the smaller diagonal block. For k = 2,…

We prove a polynomial bound in the "true complexity" problem of Gowers and Wolf. The proof uses only repeated applications of the Cauchy--Schwarz inequality, answering negatively a question posed by Gowers and Wolf. To choose and reason…

Let $A_{\alpha}^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,\alpha}$ be the algebra…

This article is about the (minimal) sector containing the numerical range of the principal part of a linear second-order elliptic differential operator defined by a form on closed subspaces V of the first-order Sobolev space…

Let $A = - \sum \partial_k \, c_{kl} \, \partial_l$ be a degenerate sectorial differential operator with complex bounded mesaurable coefficients. Let $\Omega \subset \mathds{R}^d$ be open and suppose that $A$ is strongly elliptic on…

We study the contraction semigroups of elliptic quadratic differential operators. Elliptic quadratic differential operators are the non-selfadjoint operators defined in the Weyl quantization by complex-valued elliptic quadratic symbols. We…

This paper is concerned with the final value problem for a system of nonlinear wave equations. The main issue is to solve the problem for the case where the nonlinearity is of a long range type. By assuming that the solution is spherically…