We give an example of a positive operator B in a Krein space with the following properties: the nonzero spectrum of B consists of isolated simple eigenvalues, the norms of the orthogonal spectral projections in the Krein space onto the eigenspaces of B are uniformly bounded and the point ∞ is a singular critical point of B. An operator A in the Krein space (K, [ · , · ]) is said to be positive ...

We study the rank one Harish-Chandra-Itzykson-Zuber integral in limit where \frac{N\beta}{2} \to c N?2?c , called high-temperature regime and show that it can be ...

Two concepts, evidently very different in nature, have proved to be useful in analytical and numerical studies of spectral stability in nonlinear wave theory: (i) the Krein signature of an eigenvalue, a quantity usually defined in terms of the relative orientation of certain subspaces that is capable of detecting the structural instability of imaginary eigenvalues and, hence, their potential fo...

We study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, u 4 t f t, u t , u′′ t , t ∈ 0, 1 , u 0 ∫1 0 g s u s ds, u 1 0, u′′ 0 ∫1 0 h s u ′′ s ds, u′′ 1 0, where f : 0, 1 × 0, ∞ × −∞, 0 → 0, ∞ is continuous, g, h ∈ L1 0, 1 are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the globa...

We give a short argument that for some C > 0, every n-dimensional Banach ball K admits a 256-round subquotient of dimension at least Cn/(logn). This is a weak version of Milman’s quotient of subspace theorem, which lacks the logarithmic factor. Let V be a finite-dimensional vector space over R and let V ∗ denote the dual vector space. A symmetric convex body or (Banach) ball is a compact convex...

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.

The isospectrality problem is studied for the operator of the spherical hydromagnetic α−dynamo. It is shown that this operator is formally pseudo-Hermitian (J−symmetric) and lives in a Krein space. Based on the J−symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the α−dynamo operator matrix. An in...

Flutter of an elastic body of revolution spinning about its axis of symmetry is prohibited in the subcritical spinning speed range by the Krein theorem for the Hamiltonian perturbations. Indefinite damping creates conical domains of the subcritical flutter (subcritical parametric resonance) bifurcating into the pockets of two Whitney’s umbrellas when non-conservative positional forces are addit...