bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Embeddings into the Multiplier Spaces Associated to Besov and Lizorkin-Triebel Spaces
Authors: Drihem D. , Moussai Madani
Published: September 2013

We study the set of pointwise multipliers in the Lizorkin-Triebel space

F^{s,q}_p

and of the corresponding multiplier set in the Besov space

B^{s,q}_p

, where we give sufficient conditions on the parameters

s

,

p

and

p_1

such that the embeddings

F^{n/p_1,\infty}_{p_1} \cap L^\infty \hookrightarrow M(F^{s,q}_p)

and

B^{n/p_1, \infty}_{p_1} \hookrightarrow M(B^{s,q}_p)

hold.
On the Optimality for Cascade Connection of Passive Scattering Systems and the Best Minorant Outer Function
Authors: Hang Nguyen Minh
Published: September 2013

In this paper we study passive scattering systems in the framework introduced by Arov. The main purpose is to find conditions for conserving the optimality of a cascade connection of passive scattering systems in terms of the best minorant outer function and to characterize optimal passive scattering systems which have the same transfer function.
Global Existence for some Integro-Differential Equations with Delay Subject to Non-Local Conditions
Authors: Mazouzi S. , Tatar Nasser-edine
Published: September 2013

By making use of the Leray-Schauder fixed point theorem we prove the global existence of solutions to some integro-differential equations with delay subject to non-local conditions, and this problem is considered in an arbitrary Banach space.
Riesz-Fischer Sequences and Lower Frame Bounds
Authors: Casazza Peter G. , Christensen Ole , Li Shidong , Lindner A.M.
Published: September 2013

We investigate the consequences of the lower frame condition and the lower Riesz basis condition without assuming the existence of the corresponding upper bounds. We prove that the lower frame bound is equivalent to an expansion property on a subspace of the underlying Hilbert space

\mathcal H

, and that the lower frame condition alone is not enough to obtain series representations on all of

\mathcal H

. We prove that the lower Riesz basis condition for a complete sequence implies the lower frame condition and

\omega

-independence; under an extra condition the statements are equivalent.
Pseudodifferential Operators with Analytic Symbols and Estimates for Eigenfunctions of Schrödinger Operators
Authors: Rabinovich Vladimir S.
Published: September 2013

We study the behavior of eigenfunctions of the Schrödinger operator

–\Delta + \nu

with potential having power, exponential or super-exponential growth at infinity and discontinuities on manifolds in

\mathbb R^n

. We use a connection between the domain of analyticity of the main symbol

(|\xi|^2 + \nu (x))^{–1}

of the parametrix

–\Delta + \nu

at infinity or near singularities of

\nu

and the behavior of eigenfunctions at infinity or near singularities of potentials. Our approach is based on a general calculus of pseudodifferential operators with analytic symbols.
Recovering Degenerate Kernels in Hyperbolic Integro-Differential Equations
Authors: Janno Jaan , Lorenzi Alfredo
Published: September 2013

The problem of recovering a degenerate operator kernel in a hyperbolic integro-differential operator equation is studied. Existence, uniqueness and stability for the solution are proved. A conditional convergence of a sequence of solutions corresponding to degenerate kernels to a solution corresponding to a non-degenerate kernel is shown. Such results are applied to determine space- and time-dependent relaxation kernels in a multi-dimensional viscoelastic wave equation with given boundary observations of traction type on the assumption that the kernels to be determined are representable as a finite or infinite sum of products of known space-dependent and unknown time-dependent functions.
A Unified Approach to Nonlinear Integro-Differential Inverse Problems of Parabolic Type
Authors: Colombo Fabio , Guidetti D.
Published: September 2013

We give a unified approach to a class of nonlinear parabolic inverse problems involving kernels of convolution type. Our main tools are optimal regularity results, in Sobolev and H¨older spaces, for parabolic equations and analytic semigroup theory. We apply the main abstract results (Theorems 2.1-2.2) to a model of population dynamics, to the theory of combustion of a material with memory and, finally, to a parabolic equation with elliptic part of order

2m

, which for

m

= 1 is the heat equation with memory and with non-linearity containg derivatives up to order

2m–1

.
An Extension of the Notion of Zero-Epi Maps to the Context of Topological Spaces
Authors: Furi Massimo , Vignoli A.
Published: September 2013

We introduce the class of hyper-solvable equations whose concept may be regarded as an extension to the context of topological spaces of the known notion of 0-epi maps. After collecting some notation, definitions and preliminary results we give a homotopy principle for hyper-solvable equations. We provide examples showing how these equations arise in the framework of Leray-Schauder degree, Lefschetz number theory and essential compact vector fields in the sense of A. Granas.
Oscillations for Certain Difference Equations with Continuous Variable
Authors: Zhang Binggen , Zhao Linlin
Published: September 2013

In this paper, we investigate some nonlinear difference equations with continuous variable. A linearized oscillation result is established and oscillation criteria for some forced difference equations are obtained.
Oscillation Theorems for Non-Canonical Self-Adjoint Differential Equations of Second Order
Authors: Ohriska J.
Published: September 2013

The report deals with the equation

(r(t)u'(t))' + p(t)u(t) = 0

and renders effective sufficient conditions for its oscillation and non-oscillation in the case

\int ^\infty \frac{dt}{r(t)} < \infty

.
Representation Formulas for the General Derivatives of the Fundamental Solution to the Cauchy-Riemann Operator in Clifford Analysis and Applications
Authors: Constales Denis , Kraußhar Rolf Sören
Published: September 2013

In this paper, we discuss several essentially different formulas for the general derivatives

q_n(z)

of the fundamental solution of the Cauchy-Riemann operator in Clifford Analysis, upon which – among other important applications – the theory of monogenic Eisenstein series is based. Using Fourier and plane wave decomposition methods, we obtain a compact integral representation formula over a half-space, which also lends itself to establish upper bounds on the values

\| q_n(z)\|

. A second formula that we discuss is a recurrence formula involving permutational products of hypercomplex variables by which these estimates can be obtained immediately. We further prove several formulas for

q_n(z)

in terms of explicit, non-recurrent finite sums, leading themselves to further representations in terms of permutational products but using different and fewer hypercomplex variables than used in the recurrence relations. Summing up a fixed

q_n

over a given discrete lattice leads to a variant of the Riemann zeta function. We apply one of the closed representation formulas for

q_n(z)

to express this variant of the Riemann zeta function as a finite sum of real-valued Dirichlet series.
Index Transforms Associated with Bessel and Lommel Functions
Authors: Yakubovich Semyon B.
Published: September 2013

In this paper we extend a variety of index integral transforms (i.e. integral transforms over an index as integration variable) with Bessel and Lommel functions as kernels by considering mapping properties of the related integral operators. This class of transforms includes, for instance, operators of Titchmarsh type. Useful integral representations of the considered kernels are deduced and boundedness properties, Parseval equalities, Plancherel type theorem and inversion formula are given.
Potential-Type Operators in $L^{p(x)}$ Spaces
Authors: Edmunds David E. , Meskhi Alexander
Published: September 2013

In this paper we derive weight inequalities for one-sided and Riesz potentials in

L^{p(x)}

spaces under the condition that

p

satisfies a weak Lipschitz condition. Compactness of these operators in

L^{p(x)}

spaces is also established.
$L_p-L_q$ Estimates for the Bochner-Riesz Operator of Complex Order
Authors: Karasev Denis N. , Nogin V.A.
Published: September 2013

We describe convex sets on the

(\frac{1}{p}, \frac{1}{q}

)-plane for which the well-known Bochner-Riesz operator with the symbol

(1–|\xi|^2)+^{–\alpha} (0 < \mathrm {Re} \alpha < \frac{n+1}{2})

is bounded from

L_p

into

L_q

.
Numerical Method of Lines for First Order Partial Differential-Functional Equations
Authors: Baranowska Anna , Kamont Zdzisław
Published: September 2013

We consider the Cauchy problem for a nonlinear equation on the Haar pyramid. By using a discretization with respect to spatial variables, the partial functional-differential equation is transformed into a system of ordinary functional-differential equations. We investigate the question of under what conditions the classical solutions of the original problem are approximated by solutions of associated systems of ordinary functional-differential equations. The proof of the convergence of the method of lines is based on the differentialinequalities technique. A numerical example is given. Differential equations with retarded variables and differential-integral equations are particular cases of a general model considered in the paper.
An Extended Cauchy-Kovalevskaya Problem and its Solution in Associated Spaces
Authors: Asano Kiyoshi , Tutschke Wolfgang
Published: September 2013

The classical Cauchy-Kovalevskaya problem with holomorphic intial functions is uniquely solvable provided the right-hand sides of the differential equations are holomorphic in their variables, i.e., they transform holomorphic functions into holomorphic functions. Moreover, the solutions depend holomorphically on the space-like variables. A far-reaching generalization of the Cauchy-Kovalevskaya Theorem is its abstract version which considers an abstract operator equation in a scale of Banach spaces where the behaviour of complex derivatives at the boundary is expressed by a certain mapping property of the operator under consideration in the underlying scale. Another generalization of the Cauchy-Kovalevskaya Theorem replaces the space of holomorphic functions by another so-called associated space which is defined by an elliptic operator. Making use of this second approach, the present short note solves an extended Cauchy-Kovalevskaya problem in which an initial value problem is combined with an implicit equation.
A Generalized Topological Degree in Admissible Linear Spaces
Authors: Okon T.
Published: September 2013

The paper deals with the construction of a degree which extends the Generalized Topological Degree of Browder and Petryshyn to admissible linear spaces introducing the notion of approximation nets and approximation-compact maps. After discussing the usual properties of a degree the relationship between approximation compactness and the concept of condensing maps is analysed.
An Attractor for a 3D Navier-Stokes Type Equation
Authors: Gazzola Filippo
Published: September 2013

For a modified Navier-Stokes equation existence and uniqueness results are known in the evolution 3D case: the equation considered is fully nonlinear. We investigate the main properties of the dynamical system defined by the equation: we establish the existence of an attractor, estimate the number of determining modes and prove the global stability of the stationary solution for a "small" external force.
On Solvability of a Parabolic System Arising in Physical Oceanography
Authors: Chen Senhuei
Published: September 2013

In physical oceanography, thermocline theories are to explain the phenomenon of strong, vertical density gradient in a relatively shallow layer of water where transition occurs from the ocean’s surface temperature to the colder abyss. We derive a nonlinear system of partial differential equations governing the motion of thermocline layer. Function spaces are set up to study properties of the solutions. By a local version of Banach’s fixed point theorem, the existence and smoothness of solutions are established.
An Integro-Differential Parabolic Variational Inequality Connected with the Problem of the American Option Pricing
Authors: Mastroeni Loretta , Matzeu Michele
Published: September 2013

An existence and regularity result for a linear integro-differential inequality of parabolic type, connected with the problem of the American option pricing, is stated. The proof is based on the use of some estimates of Lewy-Stampacchia type for parabolic variational inequalities and a fixed point argument.
Products of Lower Densities
Authors: Macheras N. D. , Strauss W.
Published: September 2013

We prove the existence of product-lower densities for products of arbitrary families of (possibly incomplete) probability spaces, thus generalizing the corresponding results for finite products. The proofs are based on permanence results for lower densities under projective limits of probability spaces. Relying on work of Grekas we discuss in particular Haar measures on compact groups.
Diagonalizing 'Compact' Operators on Hilbert W*-Modules
Authors: Frank Michael , Manuilov V.M.
Published: September 2013

For W*-algebras

A

and self-dual Hilbert

A

-modules

\mathcal M

we show that every self-adjoint, "compact" module operator on

\mathcal M

is diagonalizable. Some specific properties of the eigenvalues and of the eigenvectors are described.
Recurrence Coefficients of Orthogonal Polynomials with Respect to Some Self-Similar Singular Distributions
Authors: Fischer H.-J.
Published: September 2013

The limiting behaviour of arithmetic and geometric means of the coefficients of three term recurrence relations satisfied by orthogonal polynomials is investigated. The measure of orthogonality is not assumed to be absolutely continuous, but it must guarantee regular limit distribution of the zeros of the orthogonal polynomials. Some examples of self-similar distributions satisfying this condition are given.
Preservation of the Exponential Stability under Perturbations of Linear Delay Impulsive Differential Equations
Authors: Berezansky Leonid , Braverman Elena
Published: September 2013

Exponential stability of an impulsive functional-differential equation under per-turbations is studied by means of a new method. We transform a differential equation into an operator equation. The method is based on the equivalence of exponential stability and solvability of the operator equation in certain function spaces.
Some Results on Non-Coercive Variational Problems and Applications
Authors: Weissbaum F.
Published: September 2013

We give a necessary and sufficient condition to ensure the existence of solutions of three problems of the calculus of variations with non-coercive integrands. The solutions

u

we consider are lipschitz functions, i.e.

u \in W^{1, \infty} (0,1)

. The three problems depends on the same functionals but are different in the constraints. We consider respectively a problem without constraint, a problem with

u' ≥ 0

and finally a problem with

u ≥ 0

. These problems can be related to optimal foraging models in behavioural ecology.
A Convergence Rate Result for a Steepest Descent Method and a Minimal Error Method for the Solution of Nonlinear Ill-Posed Problems
Authors: Neubauer A. , Scherzer Otmar
Published: September 2013

Recently, convergence and stability of the steepest descent method for the solution of nonlinear ill-posed operator equations have been proven. The same results also hold for the minimal error method. Since for ill-posed problems the convergence of iterative methods may be arbitrarily slow, it is of practical interest to guarantee convergence rates of the iterates under reasonable assumptions. The main emphasis of this paper is to present a convergence rate result in a uniform manner for the steepest descent and the minimal error method for the noise free case.
A New Maximal Point Theorem
Authors: Göpfert Alfred , Tammer Chr.
Published: September 2013

The aim of our paper is to generalize the maximal point theorem of Bishop and Phelps and to apply this result to derive a new multicriteria Ekeland’s principle in a direct way by induction without making use of Ekeland’s original scalar result.
Vector-Valued Integration in $BK$-Spaces
Authors: Pechtl A.
Published: September 2013

Questions of convergence in

B

K-spaces, i.e. Banach spaces of complex-valued sequences

x = (x_k)_{k \in \mathbb Z}

with continuity of all functionals

x \mapsto x_k ((k \in \mathbb Z)

will be studied by methods of Fourier analysis. An elegant treatment is possible if the Cesàro sections of a

BK

-space element

x

can be represented by vector-valued Riemann integrals. This was done by Goes [2] following the example of Katznelson [5: pp. 10-12). The purpose of this paper is to make precise the conditions in [2) concerning Riemann integration and to demonstrate relations between

BK

-spaces which are generated by a given

BK

-space.
An Interpolation Problem with Symmetry and Related Questions
Authors: Alpay Daniel , Bolotnikov Vladimir , Loubaton Philippe
Published: September 2013

An interpolation problem in the class of Carathéodory functions subject to a supplementary symmetry is solved; the problem originates with the theory of periodically correlated stochastic processes. The methods used are from state space theory.
Contractive Intertwining Dilations of Quasi-Contractions
Authors: Gheondea Aurelian
Published: September 2013

We prove that quasi-contractions in Krein spaces always have contractive intertwining dilations. This result covers many of the known lifting of commutant theorems in both Hilbert and Krein spaces. The approach is an adaptation of the angular operator method and uses the existence of invariant maximal non-negative subspaces for certain operators.
A New Algebra of Periodic Generalized Functions
Authors: Valmorin V.
Published: September 2013

Let

n

denote a strictly positive integer. We construct a complex differential algebra

\mathcal G_n

of so-called

2\pi

-periodic generalized functions. We show that the space

\mathcal D^{'(n)}_{2\pi}

of

2\pi

-periodic distributions on

\mathbb R^n

can be canonically embedded into

\mathcal G_n

. Next we lay the foundation for calculation in

\mathcal G_n

. This algebra

\mathcal G_n

enables one to solve, in a canonical way, differential problems with strong singular periodic data which have no solution in

\mathcal D^{'(n)}_{2\pi}

.
Weighted Inequalities for the Fractional Integral Operators on Monotone Functions
Authors: Rakotondratsimba Y.
Published: September 2013

We give a characterization of weight functions

u

and

v

on

\mathbb R^n

for which the fractional integral operator

l_s

of order

s

on

\mathbb R^n

defined by

(I_s f)(x) = \int_{\mathbb R^n} | x - y |^{s–n} f(y)dy

sends all monotone functions which belong to the weighted Lebesgue space

L^p_v(\mathbb R^n)

into the weighted Lebesgue space

L^q_u(\mathbb R^n)

. This characterization is done for all

p

and

q

with

1 < p < \infty

and

0 < q < \infty

. The analogous Lorentz and Orlicz problems are also considered.
The Modified Canonical Proboscis
Authors: Finn Robert , Marek Jonathan
Published: September 2013

A canonical proboscis domain

\Omega

corresponding to contact angle as introduced

\gamma_0

by Fischer and Finn and later studied by Finn and Leise, has the property that a solution of the capillary problem exists in

\Omega

for contact angle

\gamma

if and only if

| \gamma – \frac{\pi}{2}| < | \gamma_0 – \frac{\pi}{2}|

. We show in this paper that every such domain can be modified so as to yield the existence of a bounded solution also at the angle

\gamma_0

. The modification can be effected in such a way that for prescribed

\epsilon > 0

the solution height must-physically become infinite when

| \gamma – \frac{\pi}{2}| > |\gamma_0 – \epsilon – \frac{\pi}{2}|

, over a subdomain that includes as large a portion of

\Omega

as desired.
A Necessary Condition to Regularity of a Boundary Point for a Degenerate Quasilinear Parabolic Equation
Authors: Leonardi S. , Skrypnik I.I.
Published: September 2013

We shall study the behaviour of solutions of the equation

v(x) \frac{\partial u}{\partial t} – \sum^n_{i=l} \frac{\partial}{\partial x_i} a_i (x, t, u \frac{\partial u}{\partial x}) = a_0 (x, t, u \frac{\partial u}{\partial x}) \\ ((x,t) \in Q_T = \Omega \times (0, T))

at a point

(x_0,t_0) \in S_T = \partial \Omega \times (0, T)

. Indeed we establish a necessary condition to the regularity of a boundary point of the cylindrical domain

Q_T

extending the analogous result from paper [13] to the degenerate case. The degeneration is given by weights (depending on the space variable) from a suitable Muchenhoupt class. It is important to note that the coefficients of the equation depend on time too.
On Multipower Equations: Some Iterative Solutions and Applications
Authors: Ruch David K. , Van Fleet Patrick J.
Published: September 2013

generalization of McFarland’s iterative scheme [12] for solving quadratic equa-tions in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this wider class of multipower equations. Existence and uniqueness of solutions are addressed within the framework of a uniformly contractive system. To illustrate the use of the new iterative scheme, we employ it when approximating solutions to a Hammerstein equation and a Chandrashekar equation. Due to the nature of the examples, we have found that wavelet/scaling function bases are a natural choice for the implementation of our iterative method.
On the Variational Stability of a Class of Nonlinear Parabolic Optimal Control Problems
Authors: Papageorgiou Nikolaos S.
Published: September 2013

In this paper we study parametric optimal control problems governed by a non-linear parabolic equation in divergence form. The parameter appears in all the data of the problem, including the partial differential operator. Using as tools the G-convergence of operators and the

\Gamma

-convergence of functionals, we show that the set-valued map of optimal pairs is upper-semicontinuous with respect to the parameter and the optimal value function responds continuously to changes of the parameter. Finally, in the case of semilinear systems we show that our framework can also incorporate systems with weakly convergent coefficients.
Monogenic Functions of Higher Spin
Authors: Sommen Franciscus
Published: September 2013

We present a definition for monogenic functions of higher spin and establish the Fischer decomposition with respect to this notion.
Local Solutions to Quasilinear Parabolic Equations without Growth Restrictions
Authors: Pluschke Volker
Published: September 2013

The paper deals with quasilinear parabolic boundary value problems where the nonlinear coefficients and right-hand side are defined with respect to the unknown function

u = u(x; t)

only in a neighbourhood of the initial function. The quasilinear parabolic problem is approximated by linear elliptic problems by means of semidiscretization in time. Itis proved that the approximations converge uniformly although the data are not continuous functions, and the limit turns out to be the weak solution of the parabolic problem for sufficiently small time

t

. The crucial points of the paper are

L_\infty

-estimates to ensure that the approximations belong to the domain of non-linearities and uniform estimates of the discrete time derivatives in a Lebesgue space in order to obtain uniform convergence.
A Numerical Range for Nonlinear Operators in Smooth Banach Spaces
Authors: Dörfner M.
Published: September 2013

The purpose of this note is to define a numerical range for nonlinear operators in smooth Banach spaces and to use this numerical range to localize certain spectral sets of Lipschitz continuous operators.
Hausdorff Dimension Estimates for Invariant Sets of Time-Dependent Vector Fields
Authors: Noack Antje , Reitmann Volker
Published: September 2013

In this paper we are concerned with generalizations of the results of A. Douady and J. Oesterlé [4] on estimates for the Hausdorff dimension of sets on Riemannian manifolds being negatively invariant with respect to a map. The main theorem that we derive for maps allows a number of corollaries which generalize several other results of A. V. Boichenko, F. Ledrappier and C. A. Leonov (see [2, 7, 8]). We extend the concept on differential equations and the corresponding vector fields on Riemannian manifolds. To obtain upper bounds for the Hausdorff dimension we formulate conditions for the eigenvalues of the symmetric part of the covariant derivative of the vector field. Modifications of the eigenvalues by the choice of an appropriate Riemannian metric will be of great importance. Besides the investigation of dimension of negatively invariant sets we are interested in the convergence behaviour of autonomous differential equations on Riemannian manifolds. We propose also a general form of the Bendixson-Dulac criterion for the non-existence of non-trivial periodic orbits of vector fields on compact Riemannian manifolds.
Convergence Structures in Numerical Analysis
Authors: Gähler Siegfried , Matel-Kaminska Donata
Published: September 2013

The paper deals — under the viewpoint of topology — with discrete Cauchy spaces, which are spaces where a discrete Cauchy structure

(t,\mathcal C)

(with

t

being a discrete convergence and

\mathcal C

being a discrete pre-Cauchy structure) is defined. More precisely, let

E_1, E_2,...

and

E

be arbitrary sets and let

\mathcal S

denote the set of all discrete sequences

(x_n,_{n \in N'}

with

x_n, \in E_n (n \in N')

and with

N'

being an infinite subset of

\mathbb N = {1,2,…}

. Then

t

and

\mathcal C

are certain subsets of

(\mathcal S, E)

respectively of

\mathcal S

, which in a certain sense are assumed to be compatible. The paper gives properties of

t

and

\mathcal C

and among others is devoted to the problem of completion of discrete Cauchy spaces

(((E_1, E_2,…), E); (t, \mathcal C))

. The construction of a completion of a discrete Cauchy space differs (in some sense essentially) from the construction of a completion of a usual sequential Cauchy space and is even more simple. An essential part of the paper is devoted to certain metric discrete Cauchy spaces, where — among others assuming that

E

is equipped with a metric

d

and that there exist mappings

q_n : E_n \to E (n \in \mathbb N)

— the discrete Cauchy structure

(t, \mathcal C)

is defined by

((x_n)_{N'}, x) \in t \Longleftrightarrow (d(q_n(x_n),x))_{N'} \to 0

(x_n)_{N'} \in \mathcal C \Longleftrightarrow (q_n (x_n))_{N'} \ \mathrm {is \ a \ Cauchy \ sequence \ in} \ (E,d).

It turns out that such a metric discrete Cauchy space is complete if and only if

(E, d)

is complete and that also the completion is metric. A further subject of the paper are metric discrete Cauchy spaces of mappings between metric discrete Cauchy spaces, where simple characterizations of the corresponding discrete convergence and discrete pre-Cauchy structure of such a discrete Cauchy space as well as a necessary and sufficient condition for its completeness are given.
A Continuation Method for Weakly Condensing Operators
Authors: O'Regan Donal
Published: September 2013

We present a continuation result for weakly condensing operators between Banach spaces. There are given also a new fixed point result being in the spirit of Schauder’s fixed point theorem and some applications to nonlinear operator equations.
Asymptotics of the Solution of an Integral Equation to Transmission Problems with Singular Perturbed Boundary
Authors: Mahnke Ralf
Published: September 2013

The integral equation to a transmission problem of the Laplacian is considered on a smooth boundary of a plane domain. The contour depends on a positive parameter e and the domain has a corner in the limit case

\epsilon = 0

. The main terms of an asymptotic expansion showing the influence of the parameter are given. The remaining part is estimated in a weak norm.
Fibonacci Polynomials their Properties and Applications
Authors: Trzaska Z.W. M.
Published: September 2013

The paper deals with polynomials characterized by coefficients determined by successive elements of the Fibonacci sequence. Basic properties and applications of the Fibonacci polynomials are demonstrated. The index of concentration of Fibonacci polynomials at

k

-th degree, locations of their zeros and optimization procedures for such polynomials are discussed. Illustrative examples are presented.
Behavior of a Bounded Non-Parametric $H$-Surface Near a Reentrant Corner
Authors: Lancaster K.E. , Siegel D.
Published: September 2013

We investigate the manner in which a non-parametric surface

z = f(x,y)

of prescribed mean curvature approaches its radial limits at a reentrant corner. We find, for example, that the solution

f(x, y)

approaches a fixed value (an extreme value of its radial limits at the corner) as a Hölder continuous function with exponent

\frac{2}{3}

as

(x,y)

approaches the reentrant corner non-tangentially from inside a distinguished half-space. We also mention an application of our results to a problem in the production of capacitors involving "dip-coating."
Hyperbolic Linear Skew-Product Semiflows
Authors: Rau R.T.
Published: September 2013

A spectral theory for evolution operators on Banach spaces has been developed in [14, 15] considering associated

C_0

-semigroups on vector-valued function spaces. It is then quite natural to substitute the shift on

\mathbb R

by an arbitrary flow

\sigma

on a topological space

X

and to substitute the evolution operator by a cocycle

\Phi

over

\sigma

. This task was performed by Latushkin and Stepin (cf. [8, 9]) for hyperbolic linear skew-product flows assuming some norm continuity of this flow. In general only strong continuity can be obtained (cf. Sacker and Sell [18) and Example 2 below). Following a suggestion by Hale [7: p. 601 we consider strongly continuous linear skew-product flows in Banach spaces and characterize hyperbolicity through a spectral condition.
Optimal Stable Solution of Cauchy Problems for Elliptic Equations
Authors: Tautenhahn Ulrich
Published: September 2013

We consider ill-posed Cauchy problems for elliptic partial differential equations

u_{tt} - Lu = 0 (0 < t ≤ T, x \in \Omega \subset \mathbb R^n)

with linear densely defined self-adjoint and positive definite operators

L : D(L) \subset H \to H

where

H

denotes a Hilbert space with norm

\| \cdot \|

and inner product

(\cdot, \cdot)

. We assume that instead of exact data

y = u(x,0)

or

y = u_t(x,0)

noisy data

y^{\delta} = u^{\delta} (x,0)

or

y^{\delta} = u(x,0)

are available, respectively, with

\|y – y^{\delta} \| ≤ \delta

. Furthermore we assume certain smoothness conditions

u(x,t) \in M

with appropriate sets

M

and answer the question concerning the best possible accuracy for identifying

u(x,t)

from the noisy data. For special sets

M

the best possible accuracy depends either in a Hölder continuous way or in a logarithmic way on the noise level

\delta

. Furthermore, we discuss special regularization methods which realize this best possible accuracy.
On the Uncertainty Principle for Positive Definite Densities
Authors: Dreier I.
Published: September 2013

The products of variances of adjoint positive definite densities have a greatest lower bound

\Lambda

. We improve the known estimates of

\Lambda

showing $0.527 < \Lambda < 0.8609....
Some Discrete Inequalities
Authors: Varošanec S. , Pečarić J. , Šunde J.
Published: September 2013

A number of inequalities with finite differences which are connected with weighted, quasiarithmetic and logarithmic means and some well-known general inequalities are considered.
About Systems of Differential Equations Related to Geodesic Double Differential Forms Mean Values and Harmonic Spaces Part I
Authors: Schuster R.
Published: September 2013

In spaces of constant curvature P. Günther has introduced geodesic double differential forms and mean value operators for differential forms. As solutions of differential equations for forms (for instance, Weyl-De Rham equations) the form equations so as the mean values suffice certain ordinary systems of differential equations. We generalize such systems and study properties which are determined by differential geometric structures (parallel translation of double differential forms with respect to geodesic lines, the construction of closed, coclosed and harmonic components of differential forms and double forms and the telescopage theorem of McKean and Singer). As special cases we get the systems known for geodesic double differential forms or mean value operators in real and complex hyperbolic spaces by the application of structural information without any special information about these spaces.
On the Integral Giving the Degree of a Map and a Rouché Type Theorem
Authors: Hatziafratis T. , Tsarpalias A.
Published: September 2013

An analytic approach to the degree of a map

f : \partial D \to \mathbb R^n \backslash \lbrace 0 \rbrace

is given (where

D \subset \mathbb R^n

is a bounded domain with smooth boundary) and a Rouché type theorem is proved.
The Character-Automorphic Nehari Problem: Non-Uniqueness Criterion and some Extremal Solutions
Authors: Yuditskii Peter
Published: September 2013

A non-uniqueness criterion for the character-automorphic Nehari problem is given. Certain subclass of solutions, connected with "the entropy functional" of the problem, is described. The description yields a character-automorphic counterpart of the Adamyan-Arov-Krein theorem.
Weighted Inequalities for the Fractional Maximal Operator in Lorentz Spaces via Atomic Decomposition of Tent Spaces
Authors: Rakotondratsimba Y.
Published: September 2013

Consider the usual fractional maximal operator

M_{\alpha}

with

0 < \alpha < n

. A characterization of

\mathbb R^n

weight functions

u(\cdot)

and

\sigma(\cdot)

for which

M_{\alpha}d\sigma

sends the (generalized) Lorentz space

\Lambda^s_{\sigma}(w_1)

into

\Lambda^r_u(w_2)

with

1 < s < r < \infty

is obtained by using a suitable-atomic decomposition of tent spaces.
Asymptotic Behaviour of Relaxed Dirichlet Problems Involving a Dirichlet-Poincaré Form
Authors: Biroli Marco , Tchou Nicoletta A.
Published: September 2013

We study the convergence of the solutions of a sequence of relaxed Dirichlet prob lems relative to Dirichlet forms to the solution of the

Γ

-limit problem. In particular we prove the strong convergence in

D^P_0[a,Ω](1≤p≤2)

and the existence of “correctors” for the strong convergence in

D_0[a,Ω]

. The above two results are generalizations to our framework of previous results proved in [10] in the usual uniformly elliptic setting.
Existence Results for the Quasistationary Motion of a Free Capillary Liquid Drop
Authors: Günther Matthias , Prokert Georg
Published: September 2013

We consider instationary creeping flow of a viscous liquid drop with free boundary driven by surface tension. This yields a nonlocal surface motion law involving the solution of the Stokes equations with Neumann boundary conditions given by the curvature of the boundary. The surface motion law is locally reformulated as a fully nonlinear parabolic (pseudodifferential) equation on a smooth manifold. Using analytic expansions, invariance properties, and a priori estimates we give, under suitable presumptions, a short-time existence and uniqueness proof for the solution of this equation in Sobolev spaces of sufficiently high order. Moreover, it is shown that if the initial shape of the drop is near the ball, then the evolution problem has a solution for all positive times which exponentially decays to the ball.
The Neumann Problem for the 2-D Helmholtz Equation in a Multiply Connected Domain with Cuts
Authors: Krutitskii P.A.
Published: September 2013

The Neumann problem for the dissipative Helmholtz equation in a connected plane region with cuts is studied. The existence of classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. It means that the solution can be computed by standard codes.
Remarks on Analytic Solutions of Leray-Volevich-Coupled Systems
Authors: Watzlawek W.
Published: September 2013

A Banach-scales approach is used for studying analytic solutions of systems of linear partial differential equations satisfying the Leray-Volevich conditions. Results on the Cauchy problem lead to a continuation result which is of the same type as the well known result of Widder [10] on analytic solutions of the heat equation.
Equivalence of Oscillation of a Class of Neutral Differential Equations and Ordinary Differential Equations
Authors: Zhang Binggen , Yang Bo
Published: September 2013

In this paper; we establish the equivalence of the oscillation of the two equations

(x(t) - x(t - r))^{(n)} + p(t) x(t - \sigma) = 0 \ \ \ \mathrm {and} \ \ \ x^{(n+1)}(t) + \frac{p(t)}{r} x(t) = 0

where

p(t) ≥ 0

and

n ≥ 1

is odd, from which we obtain some new oscillation conditions and comparison theorems for the first of these equations.
’Restricted’ Closed Graph Theorems
Authors: Boos Johann , Leiger T.
Published: September 2013

The paper deals with ’restricted’ closed’ graph theorems in the following sense: Let a suitable class

\mathcal E

of Mackey spaces as domain spaces, a class

\mathcal F

of locally convex spaces as range spaces and for each

F \in \mathcal F

a suitable class

\mathcal C_{F, \mathfrak B}

of linear maps

T : E \to F (E \in \mathcal E)

with closed graph defined by a (general) property

\mathfrak B

be given. In demand is a sufficient or even a sufficient as well as necessary condition to

F \in \mathcal F

such that each

T \in \mathcal C_{F, \mathfrak B}

is continuous. Note that in the situation of the well-known closed graph theorems of Pták and Kalton,

\mathcal E

is the class of barrelled spaces and Mackey spaces with sequentially complete weak dual space, respectively,

\mathcal F

is the class of all locally convex spaces and for each

F \in \mathcal F

the class

\mathcal C_{F, \mathfrak B}

is defined to be the set of all linear maps

T : E \to F (E \in \mathcal E)

with closed graph; a sufficient condition for

F

in the asked sense is

B_r

-completeness (Pták [10]) and to be a separable

B_r

-complete space (Kalton [8]), respectively; a sufficient as well as necessary condition for

F

is

A

-completeness (Zhu and Zhao [20]) and to be an

L_r

-space (Qiu [11], see [12] too), respectively. Based on the ideas developed in [4] and [2] in the present paper the notions of

\Theta

-completeness and of

(\Theta, F, \mathfrak B)

-spaces are introduced and a very general ’restricted’ closed graph theorem of the described type (see Theorem 2.4) is proved. Furthermore, it is shown that this main result contains both new interesting special cases and a series of known closed graph theorems, for example those due to Pták and Kalton and more generally that of Zhu and Zhao as well as that of Qiu. In addition, the paper deals with further aspects which are related to

(\Theta, \mathcal F, \mathfrak B)

-spaces and motivated by the

\varphi

-topologies introduced by Ruckle [13]. At last, the general considerations serve to extend the well-known inclusion theorems of Bennett and Kalton [1, Theorem 5 and 4] which establish a connection between functional analysis (weak sequential completeness and barrelledness) and summability.
Bifurcation from Simple Eigenvalue for Functional-Differential Equations
Authors: Stepanov Eugene
Published: September 2013

A method to determine bifurcation points of complicated boundary value problems for functional-differential equations is developed, which provides sufficient conditions on exis-tence of intervals containing bifurcation points in terms of some simple estimates rather than in terms of spectral properties of the linearized problem. In the case of Frechèt-differentiable non-linearity the method reduces to the study of bifurcation from simple eigenvalues of the lin-earized problem. It still works, if the linearized problem contains homogeneous but nonlinear operators. The heart of the approach consists in the study of branching equations obtained by Lyapunov-Schmidt reduction and a special non-equivalent change of variables. Construction of such equations based on the choice of generalized Green’s operator is discussed. At last, some applications to second order equations with deviating argument are provided.
Differentiability Properties of the Autonomous Composition Operator in Sobolev Spaces
Authors: Lanza de Cristoforis Massimo
Published: September 2013

In this paper, we study the autonomous composition operator, which takes a pair of functions

(f,g)

into its composite function

f\circ g

. We assume that

f

and

g

belong to Sobolev spaces defined on open subsets of

\mathbb R^n

, and we concentrate on the case in which the space for

g

is a Banach algebra. We give a sufficient condition in order that the composition maps bounded sets to bounded sets, and we exploit the density of the polynomial functions in the space for I in order to prove that for suitable Sobolev exponents of the spaces for

f

and

g

, the composition is continuous and differentiable with continuity up to order

r

, with

r ≥ 1

. Then we show the optimality of such conditions by means of theorems of ‘inverse’ type.
Liouville Theorems for Fuchsian-Type Operators on the Heisenberg Group
Authors: Lancia Maria Rosaria , Marchi Maria Vittoria
Published: September 2013

We prove some Liouville theorems for a degenerate elliptic operator whose principal part is given in divergence form with respect to the Heisenberg vector fields and lower terms satisfy Fuchsian-type conditions with respect to the intrinsic norm.
Oscillation and Non-Oscillation Theorems for a Class of Second Order Quasilinear Difference Equations
Authors: Thandapani E. , Arul R.
Published: September 2013

In this paper there are established necesssary and sufficient conditions for the second order quasilinear difference equation

\Delta(p_n \varphi (\Delta y_n)) + f(n,y_{n+1}) = 0 \ \ \ (n \in \mathbb N_0)

to have various types of non-oscillatory solutions. In addition, in the case that the equation is either strongly superlinear or strongly sublinear, there are established necessary and sufficient conditions for all solutions to oscillate.
Approximate Solutions for Multiple Stochastic Equations with Respect to Semimartingales
Authors: Tudor Constantin , Tudor M.
Published: September 2013

In this paper we investigate different types of approximations for a class of multi-ple stochastic equations driven by semi martingales. This class includes in particular integro-differential equations and Volterra stochastic equations.
Special Ball-Homogeneous Spaces
Authors: Calvaruso G. , Vanhecke L.
Published: September 2013

We continue the study of ball-homogeneous Riemannian manifolds, that is, R.ie-mannian spaces such that the volume of all sufficiently small geodesic balls or spheres only depends on the radius. First, we consider the case of locally reducible spaces. Then we treat the three-dimensional case, in particular for Einstein-like metrics and finally, we study confor-mally flat ball-homogeneous spaces. Our aim is to provide more partial answers to the question whether a ball-homogeneous space is locally homogeneous or not.
On Conditional Expectations Arising from Group Actions
Authors: Frank Michael , Manuilov V.M. , Troitsky E.V.
Published: September 2013

Induced conditional expectations of finite index on crossed product

C*

-algebras are considered which are non-algebraically of finite index. The characteristics of actions of (amenable) topological groups on compact Hausdorff spaces

X

are investigated, ensuring the appearance of a well-defined induced conditional expectation on the corresponding commutative

C*

-a1gebra

C(X)

and its property to be of finite index. For this purpose Hilbert

C*

-module and topological techniques are used. Special emphasis is placed on discrete group actions.
On a Theorem by W. von Wahl
Authors: Uiterdijk M.
Published: September 2013

Let

A

be the - not necessarily densely defined - generator of an analytic semigroup acting in some Banach space

X

. In the paper we prove a general theorem about the existence and uniqueness of solutions of

u’(t) = Au(t) + F(u(t))

u(0) = u_0.

Our main assumption with respect to the non-linearity is that

F

is locally Lipschitz continuous with respect to certain intermediate spaces between

\mathcal D(A)

and

X

. Our theorem extends results obtained by W. von Wahl [9] and A. Lunardi [2]. In the second part this theorem is applied to the Cahn-Hilliard equation with Dirichlet boundary conditions.
A Product for Special Classes of Monogenic Functions and Tensors
Authors: Sommen Franciscus , Van Lancker P.
Published: September 2013

In this paper we define a product for monogenic functions derived from Fischer’s decomposition. Although this product can be defined for all monogenic polynomials, it can be canonically defined only for a special subclass of polynomials. The definition of the product can be generalized to the setting of monogenic tensors.
On Uryson Operators with Partial Integrals in Lebesgue Spaces with Mixed Norm
Authors: Chen Chur-Jen , Kalitvin A.S.
Published: September 2013

IN this paper we consider some class of partial Uryson integral operators in spaces with mixed norm. We give some conditions for action, boundedness and continuity of those operators.
Complete Continuity of Some Nonlinear Volterra Operator in Banach Spaces
Authors: Väth Martin
Published: September 2013

We consider continuity and compactness of the particular Volterra operator

Hx(t) = \int ^t_{t_0} K(r)x(r)dr

, where

K(t)

is a nonlinear continuous and compact or a-Lipschitz operator in some Banach space.
Schrödinger Operators with Moving Point Perturbations and Related Solvable Models of Quantum Mechanical Systems
Authors: Geyler V.A. , Chudaev I.V.
Published: September 2013

A class of explicitly solvable models including those of low-dimensional systems in a magnetic field is considered. The spectral analysis of these models is reduced to the investigation of the spectrum of an ordinary differential operator perturbed by a point potential with varying support. The complete analysis of the variation of the eigenvalues and elgenfunctions with position of the potential support is given.
On Asymptotics for a Class of Radial Fourier Transforms
Authors: Liflyand Eli , Trebels W.
Published: September 2013

A connection is established between the multidimensional Fourier transform of a radial function

f

from a given class and the one-dimensional Fourier transform of a related function. This is applied to give an asymptotic formula for the Fourier transform of

f

. The function class in question is compared with related classes already considered in the literature.