Related papers: Class of hypocomplex structures on the two dimensi…

In this paper, we study complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we give a characterization of complex symmetric block Toeplitz operators with the special conjugation on the vector-valued Hardy…

In this paper, we consider periodic boundary value problems for differential equations whose coefficients are trigonometric polynomials. We construct the spaces of generalized functions, where such problems have solutions. In particular,…

We construct the tangential $k$-Cauchy-Fueter complexes on the right quaternionic Heisenberg group, as the quaternionic counterpart of $\overline{\partial}_b$-complex on the Heisenberg group in the theory of several complex variables. We…

The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…

Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex $\Phi$-algebras. Most notably, we improve the Cauchy-Hadamard formulas for universally complete complex…

We consider a complex of tori of length 2 defined over a number field k. We establish here some local and global duality theorems for the (\'etale or Galois) hypercohomology of such a complex. We prove the existence of a Poitou-Tate exact…

In this article, we introduce a new class of conjugations in the scalar valued Hardy space $H^2_{\mathbb{C}}(\mathbb{D})$ and provide a characterization of a complex symmetric Toeplitz operator $T_{\phi}$ with respect to these newly…

This work studies the Cauchy problem of a two-component higher order Camassa-Holm system, which is well-posed in Sobolev spaces $H^{s}(\mathbb{R})\times H^{s-2}(\mathbb{R})$, $s>\frac{7}{2}$ and its solution map is continuous. We show that…

We study the hermitean and normal two matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex…

In this paper, we study the structure of Shen-Larsson modules over the Hamiltonian Lie algebra, also known as the Lie algebra of Hamiltonian vector fields on a torus. We establish necessary and sufficient conditions for the irreducibility…

We exhibit a family of second-order hyperbolic differential operators presenting spectral transition of the Hamilton map. As a consequence we prove that the Cauchy problem is not locally solvable at the origin in Gevrey classes of order…

The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution. It is shown that the $\theta$-operator method can be used as a symbolic computational approach to…

We present complete classifications of Toeplitz + Hankel operators on vector-valued Hardy spaces and classify paired operators on $L^2(\mathbb{T})$. We also study the latter class through the lens of inner functions on the disc.

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…

This paper pursues the study of the Calabi-Yau equation on certain symplectic non-Kaehler 4-manifolds, building on a key example of Tosatti-Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a…

We extend representation formulas for functions in Hardy classes of solutions to higher-order iterated Vekua equations to Hardy classes of bicomplex-valued functions that solve a bicomplex version of the Vekua equation or its higher-order…

We study the holomorphic symplectic structures on hyper-Kaehler manifolds of type A_{\infty}, by using the torus action.

We present new results concerning the solvability, of lack thereof, in the Cauchy problem for the debar operator, with initial values assigned on a weakly pseudoconvex hypersurface, and provide illustrative examples.

We study the Cauchy problem for the advection-diffusion equation $\partial_t u + \mathrm{div} (u b ) = \Delta u$ associated with a merely integrable divergence-free vector field $b$ defined on the torus. We discuss existence, regularity and…

We review the concept of $\tau$-function for simple analytic curves. The $\tau$-function gives a formal solution to the 2D inverse potential problem and appears as the $\tau$-function of the integrable hierarchy which describes conformal…