Let M be a connected n-dimensional complex projective manifold and consider an Hermitian ample holomorphic line bundle (L, hL) on M . Suppose that the unique compatible covariant derivative ∇L on L has curvature −2πiΩ, where Ω is a Kähler form. Let G be a compact connected semisimple Lie group and μ : G×M → M a holomorphic Hamiltonian action on (M,Ω). Let g be the Lie algebra of G, and denote b...

Discrete Dirac type self-adjoint system is equivalent to the block Szegö recurrence. Representation of the fundamental solution is obtained , inverse problems on the interval and semiaxis are solved. A Borg-Marchenko type result is obtained too. Connections with the block Toeplitz matrices are treated.

The classical Szegö theorems study the asymptotic behaviour of the determinants of the finite sections PnT (a)Pn of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.

In this paper, we study the relations between the log term of the Szegö kernel of the unit circle bundle of the dual line bundle of an ample line bundle over a compact Kähler manifold. We prove a local rigidity theorem. The result is related to the classical Ramadanov conjecture.

We consider statistical aspects of the modelling and prediction theory of time series in one and many dimensions. We discuss Lévy-based and general models, and the stationary and non-stationary cases. Our starting point is the recent pair of surveys, Szegö’s theorem and its probabilistic descendants and Multivariate prediction and matrix Szegö theory, by this author.

We give general integral formulas involving for hyperdeterminants or hyperpfaffians. In the applications, we obtain several summation formulas for the products of Schur functions, which are generalizations of Cauchy’s determinant. Further, we study Toeplitz hyperdeterminants by using the theory of Jack polynomials and give a hyperdeterminant version of a strong Szegö limit theorem. MSC-class: p...

We study the adaptive decomposition of functions in the monogenic Hardy spaces H2 by higher order Szegö kernels under the framework of Clifford algebra and Clifford analysis, in the context of unit ball and half space. This is a sequel and a higher-dimensional generalization of our recent study on the complex Hardy spaces.