Browder spectra of upper-triangular operator matrices

Let be a 2×2 upper triangular operator matrix acting on the Hilbert space H⊕K. In this paper, for given operators A and B, we prove that

     

A combinatorial identity with application to Catalan numbers

By a very simple argument, we prove that if l,m,n∈{0,1,2,…} then

     

Boundary blow-up solutions with a spike layer

We prove that for large λ>0, the boundary blow-up problem

     

Concentration of mass on the Schatten classes

Let 1?p?∞ and be the unit ball of the Schatten trace class of matrices on Cn or on Rn, normalized to have Lebesgue measure equal to one. We prove that

     

Infinitely many periodic solution orbits of autonomous Lagrangian systems on tori

We prove that for any τ>0 the autonomous Lagrangian system

     

Perturbation from Dirichlet problem involving oscillating nonlinearities

In this paper we prove that if the potential has a suitable oscillating behavior in any neighborhood of the origin (respectively +∞), then under very mild conditions on the perturbation term g, for every k∈N there exists bk>0 such that

     

Positive solutions to sublinear second-order divergence type elliptic equations in cone-like domains

We study the existence and nonexistence of positive solutions to a sublinear (p<1) second-order divergence type elliptic equation in unbounded cone-like domains CΩ. We prove the existence of the critical exponent

     

A note on the edge cover number and independence number in hypergraphs

Consider a hypergraph of rank r>2 with m edges, independence number α and edge cover number ρ. We prove the inequality

     

Improved Poincaré inequalities with weights

In this paper we prove that if Ω∈Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:

     

Norm estimates of almost Mathieu operators

We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C^*-algebra . In the process, we prove for every λ∈R and the inequality

     

Precise rates in the law of the logarithm in the Hilbert space

Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X₁+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,

     

On the existence of universal series by trigonometric system

In this paper we prove the following: let ω(t) be a continuous function, increasing in [0,∞) and ω(+0)=0. Then there exists a series of the form

     

On small fractional parts of polynomials

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We prove that for any real polynomial f(x)∈R[x] the set

     

Additivity of Jordan maps on standard Jordan operator algebras

Let A be a standard Jordan operator algebra on a Hilbert space of dimension >1 and B be an arbitrary Jordan algebra. In this note, we prove that if a bijection ?:A→B satisfies

     

On the maximal order of numbers in the “factorisatio numerorum” problem

Let m(n) be the number of ordered factorizations of n?1 in factors larger than 1. We prove that for every ε>0

     

Linear independence of values of Tschakaloff functions with different parameters

We prove Q-linear independence results for the values of the q-series

     

Browder spectra for upper triangular operator matrices

When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space H⊕K of the form . In this paper, we prove that

     

The stability of the equilibrium of the damped oscillator with damping changing sign

In this paper, we prove a sufficient and necessary condition for the stability of the equilibrium x=x^′=0 of the damped oscillator with damping changing sign

     

Minimal pseudocompact group topologies on free abelian groups

A Hausdorff topological group G is minimal if every continuous isomorphism f:G→H between G and a Hausdorff topological group H is open. Significantly strengthening a 1981 result of Stoyanov, we prove the following theorem: For every infinite minimal abelian group G there exists a sequence of cardinals such that