where 〈·, ·〉 denotes the standard inner product on C. If the Hermitian matrix H is invertible, then the indefinite inner product is nondegenerate. In that case, for every matrix T ∈ C, there is the unique matrix T [∗] satisfying [T x, y] = [x, T y] for all x, y ∈ C, and it is given by T [∗] = HT H . In these spaces, the notion of H-quasihyponormal matrix can be introduced by analogy with the qu...

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express th...

The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random eigenproblems are presented an...

Several inequalities for gramian normal operators and for gramian self-adjoint operators in pseudo-Hilbert spaces are presented.

In this paper, we considered the problem of finding the upper bound Haus-dorff matrix operator from sequence spaces l p (v) (or d(v, p)) into l p (w) (or d(w, p)). Also we considered the upper bound problem for matrix operators from d(v, 1) into d(w, 1), and matrix operators from e(w, ∞) into e(v, ∞), and deduce upper bound for Cesaro, Copson and Hilbert matrix operators, which are recently con...

We write S∞ to denote the unit sphere of `, the set of all z in ` for which 〈z, z〉 = 1 (this set is often called the complex Hilbert sphere). A continuous complex-valued function f defined on the closed unit disc D := {ζ ∈ C : |ζ| ≤ 1} is said to be positive definite of order n on S∞ if, for any set of n distinct points z1, . . . , zn on S∞, the n×n matrix A with ij-entry given by f(〈zi, zj〉) i...

Cryptography protects users by providing functionality for the encryption of data and authentication of other users. This technology lets the receiver of an electronic message verify the sender, ensures that a message can be read only by the intended person, and assures the recipient that a message has not be altered in transit. Classical cryptanalysis involves an interesting combination of ana...

In 2004, J.-C. Aval, F. Bergeron and N. Bergeron studied the algebra of diagonally quasi-symmetric functions DQSym in the ring Q[x,y] with two sets of variables. They made conjectures on the structure of the quotient Q[x,y]/〈DQSym〉, which is a quasi-symmetric analogue of the diagonal harmonic polynomials. In this paper, we construct a Hilbert basis for this quotient when there are infinitely ma...

We propose that for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an “elliptic” identification provides a concrete realization of observer complementarity in de Sitter space: every observer has complete information. This proposal naturally leads to a holographic description in which the dual (conformal) field theory lives on a single sphere. Correlation fu...