Related papers: Fourier integrals and a new representation of Masl…
Let $M$ be a manifold and $\Lambda$ a compact exact connected Lagrangian submanifold of $T^*M$. We can associate with $\Lambda$ a conic Lagrangian submanifold $\Lambda'$ of $T^*(M\times R)$. We prove that there exists a canonical sheaf $F$…
For a holomorphic family of classical pseudodifferential operators on a closed manifold we give exact formulae for all coefficients in the Laurent expansion of its Kontsevich-Vishik canonical trace. This generalizes a known result…
We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our techniques, we prove uniform bounds for oscillatory Carleson…
We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.
In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of…
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog and…
We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…
We consider the geometry of second order linear operators acting on the commutative algebra of densities on a (super)manifold introduced in our previous work. In the conventional language, operators on the algebra of densities correspond to…
We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through…
We introduce and study a family of integral operators in the Kantorovich sense for functions acting on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform…
We refine a method for finding a canonical form for symmetry operators of arbitrary order for the Schroedinger eigenvalue equation on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal…
Shortcomings of Dirac's constrained analysis in the context of fourth order Pais-Uhlenbeck oscillator action and the appearance of badly affected phase-space Hamiltonian for a generalized fourth order oscillator action, following…
We show how a method to construct canonical differential equations for multi-loop Feynman integrals recently introduced by some of the authors can be extended to cases where the associated geometry is of Calabi-Yau type and even beyond.…
This article is concerned with the semi-classical limits of matrix elements $<F \phi_j, \phi_j>$ of eigenfunctions of the Laplacian $\Delta_g$ of a compact Riemannian manifold $(M, g)$ with respect to a Fourier integral operator $F$ on…
We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).
$C_{\lambda}$-extended oscillator algebras generalizing the Calogero-Vasiliev algebra, where $C_{\lambda}$ is the cyclic group of order $\lambda$, are studied both from mathematical and applied viewpoints. Casimir operators of the algebras…
It is shown that the SO(3) isometries of the Euclidean Taub-NUT space combine a linear three-dimensional representation with one induced by a SO(2) subgroup, giving the transformation law of the fourth coordinate under rotations. This…
Feynman integrals whose associated geometries extend beyond the Riemann sphere, such as elliptic curves and Calabi-Yau varieties, are increasingly relevant in modern precision calculations. They arise not only in collider cross-section…
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine…
We prove, by use of inductive techniques, that assorted unbounded composition operators in $L^2$-spaces with matrical symbols are cosubnormal.