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The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a complex vector space, which is a generalization of the discrete-time…
Consider a component Q of a stratum in the moduli space of area one abelian differentials on a surface of genus g. Call a property P for periodic orbits of the Teichmueller flow typical if the growth rate of orbits with this property is…
We treat the eigenvalue problem posed by self-similar potentials, i.e. homogeneous functions under a particular affine transformation, by means of symmetry techniques. We find that the eigenfunctions of such problems are localized, even…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
We study the group of interval exchange transformations. Let $T$ be an $m$-interval exchange transformation. By the rank of $T$ we mean the dimension of the $\mathbb{Q}$-vector space spanned by the lengths of the exchanged subintervals. We…
We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function satisfies a suitable convexity condition. These…
Spectrum of a certain class of first order conformally invariant operators on the sphere is explicitly computed. The class contains the (elliptic verions of) Rarita-Schwinger operator and its higher spin analogues.
We study a class of potentials $f$ on one sided full shift spaces over finite or countable alphabets, called potentials of product type. We obtain explicit formulae for the leading eigenvalue, the eigenfunction (which may be discontinuous)…
We investigate the classical eigenvalue problem that arises in hydrodynamics and is referred to as the sloshing problem. It describes free liquid oscillations in a liquid container W in R^3. We study the case when W is an axially symmetric,…
We construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under…
This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimensional Hilbert space. This approach is both motivated by…
We derive, under a technical assumption, the first variation formula for the eigenvalues of the Laplacian on a closed manifold evolving by the Ricci flow and give some applications.
In this paper we study the exponential functionals of the processes $X$ with independent increments , namely $$I_t= \int _0^t\exp(-X_s)ds, _,\,\, t\geq 0,$$ and also $$I_{\infty}= \int _0^{\infty}\exp(-X_s)ds.$$ When $X$ is a…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the…
We consider nonregular graphs having precisely three distinct eigenvalues. The focus is mainly on the case of graphs having two distinct valencies and our results include constructions of new examples, structure theorems, valency…
In this paper we study the eigenvalues of Hermitian Toeplitz matrices with the entries $2,-1,0,\ldots,0,-\alpha$ in the first column. Notice that the generating symbol depends on the order $n$ of the matrix. If $|\alpha|\le 1$, then the…
We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions consisting the equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our results are…
In this note, we establish certain regularity estimates for the spinor flow introduced and initially studied in \cite{AWW2016}. Consequently, we obtain that the norm of the second order covariant derivative of the spinor field becoming…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…