Related papers: Formal confluence of quantum differential operator…
We give a short new proof for the theorem that global sections of the sheaf of quantum differential operators on a quantum flag manifold are given by the quantum group. As corollaries we retrieve Joseph and Letzter's quantum versions of…
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the…
We show that an elliptic uniform pseudodifferential operator over a manifold of bounded geometry defines a class in uniform K-homology, and that this class only depends on the principal symbol of the operator.
We study the regularity of the solution to an obstacle problem for a class of integro-differential operators. The differential part is a second order elliptic operator, whereas the nonlocal part is given by the integral fractional…
This text can be considered as a non-technical and arithmetically motivated introduction to the definition of the limiting mixed Hodge structure. We state several assertions in terms natural to the classical theory of ordinary differential…
We study the Hp-Lq boundedness of certain integral operators of fractional type.
In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…
We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal…
We propose solutions of the quantum Q-systems of types $B_N,C_N,D_N$ in terms of $q$-difference operators, generalizing our previous construction for the Q-system of type $A$. The difference operators are interpreted as $q$-Whittaker limits…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operators and by the boundary conditions. We review some modern…
Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…
This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type $1,1$ in H\"ormander's sense. Thus, it contributes to the long-standing problem of…
Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous…
Quantum annealing is a promising method for solving combinational optimization problems and performing quantum chemical calculations. The main sources of errors in quantum annealing are the effects of decoherence and non-adiabatic…
We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique are then used to describe all maximal…
We provide a full characterisation of quantum differentiability (in the sense of Connes) on quantum tori. We also prove a quantum integration formula which differs substantially from the commutative case.
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
We construct the number operator for particles obeying infinite statistics, defined by a generalized q-deformation of the Heisenberg algebra, and prove the positivity of the norm of linearly independent state vectors.