We consider the algebra A of bounded operators on L 2 (R n) generated by quantizations of
isometric affine canonical transformations. The algebra A includes as subalgebras …

We define a representation of the unitary group U (n) by metaplectic operators acting on L2
(Rn) and consider the operator algebra generated by the operators of the representation …

We develop a local index theory for a class of operators associated with non-proper and non-
isometric actions of Lie groupoids on smooth submersions. Such actions imply the existence …

We consider an algebra A of Fourier integral operators on R n. It consists of all operators D:
S (R n)→ S (R n) on the Schwartz space S (R n) that can be written as finite sums (1) D=∑ R …

Let $\Gamma $ be a compact group acting on a smooth, compact manifold $ M $, let $
P\in\psi^ m (M; E_0, E_1) $ be a $\Gamma $-invariant, classical pseudodifferential operator …

We study the Fredholm solvability for a new class of nonlocal boundary value problems
associated with group actions on smooth manifolds. Namely, we consider the case in which …

We study boundary value problems for the wave equation with conditions on the entire
boundary and obtain sufficient conditions for the Fredholm solvability of the problem in …

We consider an algebra $\mathscr A $ of Fourier integral operators on $\mathbb R^ n $. It
consists of all operators $ D:\mathscr S (\mathbb R^ n)\to\mathscr S (\mathbb R^ n) $ on the …

In the paper, the ellipticity (Fredholm property) of operators of the form D_0+ D_1 Φ is
investigated, where D_0, D_1 are pseudodifferential operators of Shubin type and Φ is a …

We consider semiclassical operators equal to linear combinations of quantized canonical
transformations with pseudodifferential operators as coefficients and study semiclassical …