相关论文: The Delsarte-Darboux type binary transformations a…
For lattice operators that are relevant to the calculation of moments of nucleon structure functions we investigate the transformation properties under the hypercubic group. We give explicit bases of irreducible subspaces for tensors of…
We consider non-twisted meromorphic connections in $\mathfrak{sl}_2(\mathbb{C})$ and the associated symplectic Hamiltonian structure. In particular, we provide explicit expressions of the Lax pair in the geometric gauge supplementing…
Darboux transformations are non-group type symmetries of linear differential operators. One can define Darboux transformations algebraically by the intertwining relation $ML=L_1M$ or the intertwining relation $ML=L_1N$ in the cases when the…
Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following:…
We study discrete (duality) symmetries of functional determinants. An exact transformation of the effective action under the inversion of background fields $\beta (x) \to \beta^{-1}(x)$ is found. We show that in many cases this inversion…
Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form.…
It is shown that a pair of Hilbert space operators V and W such that V*W=I (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal basis are replaced with biorthogonal sequences, and it is also…
We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…
For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation $RLL=LLR$, the trace of the L-operator gives a…
We consider a classical problem of Computer Algebra: symbolic solution of PDEs. We transform the famous Darboux theorems on differential transformations of hyperbolic operator into the space of invariants. We introduce a new idea -- $X$-…
Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $ \delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot \beta} {\overline c}^{\dot…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend known results for orthogonal polynomials and can be used to…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
With respect to the Dirac operator and the conformally invariant Laplacian, an explicit description of the inverse Penrose transform on Riemannian twistor spaces is given. A Dolbeault representative of cohomology on the twistor space is…
In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under…