Related papers: The Determinant Line Bundle for Fredholm Operators…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
We construct and give a complete classification of all the differential symmetry breaking operators D_{{\lambda},{\nu}}^m : C^\infty(S^3, V^3_{\lambda}) \rightarrow C^\infty(S^2,L_{m,{\nu}}), between the spaces of smooth sections of a…
We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the $L^2$-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and…
We consider Fredholm determinants of matrix convolution operators associated to matrix versions of the $n - $th Airy functions. Using the theory of integrable operators, we relate them to a fully noncommutative Painlev\'e II hierarchy,…
Let $(-A,B,C)$ be a linear system in continuous time $t>0$ with input and output space ${\mathbb C}$ and state space $H$. The scattering (or impulse response) functions $\phi_{(x)}(t)=Ce^{-(t+2x)A}B$ determines a Hankel integral operator…
The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give…
In this paper, we established Fredholm theory of the linearized ${{\bar \partial}}$-operator and studied the additivity of its index.
The index of a selfadjoint Fredholm operator is zero by the well-known fact that the kernel of a selfadjoint operator is perpendicular to its range. The Fredholm index was generalised to families by Atiyah and J\"anich in the sixties, and…
For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…
We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs…
We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local…
Let $X \rightarrow S$ be a smooth projective surjective morphism, where $X$ and $S$ are integral schemes over complex numbers. Let L_0, L_1, .... L_{n-1}, L_{n} be line bundles over $X$. There is a natural isomorphism of the Deligne pairing…
We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…
We exhibit how the Hodge-Deligne moduli space of $\lambda$-connections over a smooth projective curve, for stable bundles with fixed determinant, can be understood as the dual of the Atiyah algebroid of the determinant of cohomology line…
In this note, we study linear determinantal representations of smooth plane cubics over finite fields. We give an explicit formula of linear determinantal representations corresponding to rational points. Using Schoof's formula, we count…
To a symmetric, relatively ample line bundle on an abelian scheme one can associate a linear combination of the determinant bundle and the relative canonical bundle, which is a torsion element in the Picard group of the base. We improve the…
We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.
We study the stability of Fredholm property for regular operators on Hilbert $C^*$-modules under some certain perturbations. We treat this problem when perturbing operators are (relatively) bounded or relatively compact. We also consider…
In this paper, we define and index for continuous families of semi-Fredholm bounded liner operators. Moreover, we study various regularities and semiregularities of continuous families of bounded linear operators.
In this paper, we give new characterizations of monopole bundle systems of complex hypermanifolds in $n$-dimensional spaces for certain classes of operators. In particular, we consider the reproducing kernels for decomposable polynomials of…