Related papers: Bilinear gauge operators
We introduce multilinear operators, that generalize Hirota's bilinear $D$ operator, based on the principle of gauge invariance of the $\tau$ functions. We show that these operators can be constructed systematically using the bilinear $D$'s…
We consider multilinear generalization of the Hirota derivative, which serves as a building block for integrable solitonic hierarchies. 2 special integrable mutlilinear equations are shown to be splittable into pairs of bilinear operators,…
In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the…
In this paper we go deep into the connection between duality and fields redefinition for general bilinear models involving the 1-form gauge field $A$. A duality operator is fixed based on "gauge embedding" procedure. Dual models are shown…
An interpretation of Hirota bilinear relations for classical $\tau$ functions is given in terms of intertwining operators. Noncommutative example of $U_q(sl_2)$ is presented.
In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators…
We study the bilinear fractional integral considered by Kenig and Stein, where linear combinations of variables with matrix coefficients are involved. Under more general settings, we give a complete characterization of the corresponding…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
We introduce Wirtinger operators for functions of several quaternionic variables. These operators are real linear partial differential operators which behave well on quaternionic polynomials, with properties analogous to the ones satisfied…
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials.…
Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials associated with Calogero-Sutherland type…
This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$.
Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional…
We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…
Divided difference operators are degree-reducing operators on the cohomology of flag varieties that are used to compute algebraic invariants of the ring (for instance, structure constants). We identify divided difference operators on the…
By applying the derivative operator to the corresponding hypergeometric form of a $q$-series transformation due to Andrews [1,Theorem 4], we establish a general harmonic number identity. As the special cases of it, several interesting…
We discuss boundedness properties of certain classes of discrete bilinear operators that are similar to those of the continuous bilinear pseudodifferential operators with symbols in the H\"ormander classes $BS^{\omega}_{1, 0}$. In…
Commutators of bilinear pseudodifferential operators with symbols in the H\"ormander class BS_{1, 0}^1 and multiplication by Lipschitz functions are shown to be bilinear Calder\'on-Zygmund operators. A connection with a notion of…
We follow the general recipe for constructing commutative families of $W$-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to…
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…