bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Quadrature Method for the Singular Integral Equation on Curves with Corner Points
Authors: Buehring Kathrin 
Published: May 2007

AbstractThis paper is concerned with a quadrature method for the approximate solution of the singular integral equation magnified image on the closed curve Γ with a finite number of corner points. Here 𝒶 and 𝒷 are piecewise continuous functions on Γ. We establish necessary and sufficient conditions for the stability of the quadrature method and, in addition, derive the convergence rates. For this we shall apply techniques similar to those used in the case where Γ is an interval (cf. [8]). The crucial point is a change of the variables depending on a parameter and a subsequent application of a simple quadrature rule on a uniform grid.
On Vector‐valued Inequalities of the Marcinkiewicz‐Zygmund, Herz and Krivine Type
Authors: Gasch J. , Maligranda L. 
Published: May 2007

AbstractAny continuous linear operator T: Lp → Lq has a natural vector‐valued extension T: Lp(l) → Lq(l) which is automatically continuous. Relations between the norms of these operators in the cases of p = q and r = 2 were considered by Marcinkiewicz‐Zygmund [28], Herz [14] and Krivine [19] ‐ [21]. In this paper we study systematically these relations and given some applications. It turns out that some known results can be proved in a simple way as a consequence of these developments.
Entropy Numbers in Weighted Function Spaces and Eigenvalue Distributions of Some Degenerate Pseudodifferential Operators I
Authors: Haroske Dorothee , Triebel Hans 
Published: May 2007

AbstractIn this paper we study weighted function spaces of type B(ℝn, Q(x)) and F(ℝn, Q(x)), where Q(x) is a weight function of at most polynomial growth. Of special interest are the weight functions Q(x) = (1 + |x|2)α/2 with α ϵ ℝ. The main result deals with estimates for the entropy numbers of compact embeddings between spaces of this type.
Asymptotic Properties of N‐th Order Differential Equations with Delayed Argument
Authors: Džurina Jozef 
Published: May 2007

AbstractThe aim of this paper is to deduce oscillatory and asymptotic behaviour of delay differential equationLnu(t)– P(t)u(τ(t))= 0 from the oscillation of a set of the first order delay differential equations with larger deviating argument of the formy′(t)+ qi(t) y(w(t)) = 0.
Inclusions and Identities for the Moore‐Penrose Inverse of a Closed Linear Operator
Authors: Groetsch C. W. 
Published: May 2007

AbstractA number of operator inclusions, and identities, involving the Moore‐Penrose inverse of a closed densely defined linear operator, are presented. Some of these inclusions generalize known identities in the case when the operator is bounded and has closed range. An application to a known compactness criterion for the Moore‐Penrose inverse is also given.
A Noncharacteristic Cauchy Problem for Linear Parabolic Equations I: Solvability
Authors: Haò Dinh Nho 
Published: May 2007

AbstractNoncharacteristic Cauchy problems for parabolic equations arc frequently encountered in many areas of heat transfer. These problems are well known to be severely ill‐posed. In this paper a solvability criterion for a class of such problems is established. It is proved that a weak solution of a noncharacteristic Cauchy problem for linear parabolic equations in divergence form with coefficients in a Holmgren class 2 in time exists if and only if the Cauchy data arc functions of a Holmgren class 2! A function g(t) defined on (α, β) is said to be of a Holmgren class 2, if g ϵC∞ (α, β) and for all nonnegative integers n there exist positive constants c and s such that |g(n)| < csn(2n)!.
Eigenvalue Inequalities and Schubert Calculus
Authors: Helmke Uwe , Rosenthal Joachim 
Published: May 2007

AbstractUsing techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A1,…, Ar ϵ ¢n×n with the spectrum of the sum A1 + … + Ar. These extend eigenvalue inequalities due to Freede‐Thompson and Horn for sums of eigenvalues of two Hermitian matrices.
Complex Interpolation of Hardy‐Type Subspaces
Authors: Kalton N. J. 
Published: May 2007

AbstractWe consider the problem of complex interpolation of certain Hardy‐type subspaces of Köthe function spaces. For example, suppose that X0 and X1 arc Köthe function spaces on the unit circle T. and let HX0 and HX1 be the corresponding Hardy spaces. Under mild conditions on X0. X1 we give a necessary and sufficient condition for the complex interpolation space [HX0. HX1]0 to coincide with HX0 where HX0 = [H0. H1]0. We develop a very general framework for such results and our methods apply to many more general situations including the vector–valued case.
Sommerfeld Half‐plane Problems with Higher Order Boundary Conditions
Authors: Santos P. A. , Teixeira F. S. 
Published: May 2007

AbstractSommerfeld‐type diffraction problems for a half‐plane with arbitrary n‐th order generalized impedance boundary conditions arc examined in a Sobolev space setting. The corresponding boundary‐transmission problems for the two dimensional Helmholtz equation are shown to be well‐posed in a family of Sobolev spaces with finite energy norms, through a reduction to equivalent systems of boundary integral equations of Wiener‐Hopf type in [L2+ (IR)]2. Formulas for the solutions as well as the so‐called edge conditions arc obtained for any n, by explicit canonical generalized factorization of the presymbols of the associated Wiener‐Hopf operators.
On the Two‐step Newton Method for the Solution of Nonlinear Operator Equations
Authors: Appell J. , De Pascale E. , Evkhuta N. A. , Zabrejko P. P. 
Published: May 2007

AbstractBuilding on the method of Kantorovich majorants, we give convergence results and error estimates for the two‐step Newton method for the approximate solution of a nonlinear operator equation.
The Nonclassical Boundary‐contact Problems of Elasticity for Homogeneous Anisotropic Media
Authors: Chkadua O. O. 
Published: May 2007

AbstractThe existence and uniqueness of solutions of the nonclassical boundary‐contact problems (i.e., problems with a contact on some part of the boundaries) of elasticity for homogeneous anisotropic media are investigated in Besov and Bessel potential spaces using methods of potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied.
Invariant Inner Ideals in W*‐algebras
Authors: Edwards C. M. , Rüttimann G. T. , Yu. Vasilovsky S. 
Published: May 2007

AbstractLet H(B,α) be the JBW*‐algebra of elements of a continuous W*‐algebra B invariant under the *‐anti‐automorphism α of B of order two. Then the mapping I → I ∩ H(B, α) is an order isomorphism from the complete lattice of α‐invariant weak* closed inner ideals in B onto the complete lattice of weak* closed inner ideals in H(B, α), every one of which is of the form eH(B, α) α(e) for some unique projection e in B with α‐invariant central support. A corollary of this result completely characterizes the weak* closed inner ideals in any continuous JBW*‐triple.
Weighted Inequalities for Monotone Functions
Authors: García Alejandro 
Published: May 2007

AbstractWeighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi‐linear operators on monotone functions. Several properties of the classes B(p, n) and C(p, n) introduced by Neugebauer in [13] are given. In particular, we characterize the weight pairs w, v for which \documentclass{article}\pagestyle{empty}\begin{document}$ \int\limits_0^\infty {f(x)^p w(x)dx \le C \int\limits_0^\infty {({\textstyle{1 \over x}}\int\limits_0^x f)^p } v(x) dx,} $\end{document} for nondecreasing functions f and 1 ≦ p < ∞.
Long‐Time Behaviour of Langevin Algorithms with Time‐dependent Energy Function
Authors: Grillo Gabriele 
Published: May 2007

AbstractWe study the Langevin algorithm on C∞ n‐dimensional compact connected Riemannian manifolds and on IRn, allowing the energy function U to vary with time. We find conditions under which the distribution of the process at hand becomes indistinguishable as t → ∞ from the “instantaneous” equilibrium distribution. Such conditions do not necessarily imply that U(t) converges pointwise as t → ∞.
O*‐algebras in Standard System
Authors: Inoue Atsushi 
Published: May 2007

AbstractIn the previous papers [10, 12] we have defined and studied the notion of standard generalized vectors which makes possible to develop the Tomita‐Takesaki theory in algebras of unbounded operators called O*‐algebras. The main purpose of this paper is to consider when an O*‐algebra is algebraically or spatially isomorphic to an O*‐algebra with a standard generalized vector.
Determining the Monogeneity of a Quartic Number Field
Authors: Koppenhöfer David 
Published: May 2007

AbstractThis note presents a method that determines all power integral bases of a quartic number field by solving Thue equations of degrees 3 and 4. To this end, projective representations of the ring of integers by graded complete intersections are studied and a criterion for monogeneity in terms of projective representations is derived.
Fredholm Theory for a Class of Singular Integral Operators with Carleman Shift and Unbounded Coefficients
Authors: Kravchenko V. G. , Lebre A. B. , Litvinchuk G. S. , Teixeira F. S. 
Published: May 2007

AbstractA criterion for the Fredholmness of singular integral operators with Carleman shift in LP(Γ) is obtained, where Γ is either the unit circle or the real line. The approach allows to consider unbounded coefficients in a class related to that of quasicontinuous functions. Applications to Wiener‐Hopf‐Hankel type operators and operators with linear fractional Carleman shift on IR are included.
Maximal Probability Inequalities for Stochastic Processes
Authors: Móricz F. 
Published: May 2007

AbstractLet Xa,b be nonnegative random variables with the property that Xa,b ≦ Xa,c + Xc.b for all 0≦ a < c < b ≦ T, where T > 0 is fixed. We define Ma,b = sup {Xa,c: a < c ≦ h} and establish bounds for P[Ma,b ≧ λ] in terms of given bounds for P[Xa,b ≧ λ], where λ runs through some interval (0, λo), 0 < λo ≦ ∞ fixed. These bounds explicitly involve a nonnegative function g(a, b) assumed to be quasi‐superadditive with an index Q, i.e., g(a, c) + g(c, b) ≦ Qg(a, b) for all 0≦ a < c < b < T, where 1 ≦ Q < 2 is fixed.Maximal inequalities obtained in this way can be applied to stochastic processes exhibiting long‐range dependence. Among others, these applications may include certain self‐similar processes such as fractional Brownian motion, stochastic processes occurring in linear time series models, etc.
Asymptotic Analysis of the Lyapunov Exponents of Certain Linear Hamiltonian Systems with Small Noise
Authors: Teichert Heidrun 
Published: May 2007

AbstractIn the paper there are considered linear Hamiltonian systems in R2n which include a small additive random term depending on a stationary ergodic Markov process. Under some regularity assumptions we derive asymptotic expansions for certain Lyapunov exponents of the systems (or for sums of them). The method used here is also applicable to the asymptotic analysis of a generalized rotation number.
Square Powers of Singularly Perturbed Operators
Authors: Albeverio Sergio , Karwowski Witold , Koshmanenko Vladimir 
Published: May 2007

AbstractWe use the method of self‐adjoint extensions to define a self‐adjoint operator AT as the singular perturbation of a given self‐adjoint operator A by a singular operator T on a Hilbert space.We also find the structure of a singular operator Q such that the singular perturbation of A2 by Q satisfies (A2)Q = (AT)2. We obtain the explicit form of Q in terms of A and T. A definition of the n‐th power for strictly positive symmetric operators is also given.
Bögel Functions, Tensor Products and Blending Approximation
Authors: Badea C. , Cottin C. , Gonska H. H. 
Published: May 2007

AbstractFor two compact metric spaces X and Y, we prove that the space of all bounded Bögel functions on X × Y is isometrically isomorphic with the completion of the blending function space M(X) ⊗ C(Y)+ C(X) ⊗ M(Y) with respect to a suitable norm. This solves a problem raised by G. Freud. Here M(Z) and C(Z) denote the spaces of all bounded and continuous functions on the metric space Z, respectively. Applications are given to some problems in so‐called blending approximation. All this is based on an abstract Jackson‐type theorem in terms of the entropy numbers of X and Y and the mixed modulus of smoothness.
Finite Interval Convolution Operators on the Bessel Potential Spaces H
Authors: Bastos M. A. , Dos Santos A. F. , Duduchava R. 
Published: May 2007

AbstractFinite interval convolution operators acting between Bessel potential spaces Hsp are studied in regard to Fredholm properties and invertibility. The Fourier transform of the kernel‐function of the operator is assumed to be piecewise continuous on R. An example from diffraction theory is included.
Method of Discrepancy in Interpolation Spaces for Nonlinear Ill‐posed Problems
Authors: Buong Nguyen 
Published: May 2007

AbstractIn this note we study a variational method of regularization to solve nonlinear ill‐posed problems involving monotone operators in infinite dimensional Banach space, when perturbative operators are non ‐ monotone, basing on minimization of norm in interpolation space over closed and convex sets.
Operator Ranges in Banach Spaces, I
Authors: Cross R. W. , Ostrovskii M. I. , Shevchik V. V. 
Published: May 2007

AbstractLet X be a Banach space. A subspace L of X is called an operator range if there exists a continuous linear operator T defined on some Banach space Y and such that TY = L. If Y = X then L is called an endomorphism range. The paper investigates operator ranges under the following perspectives: (1) Existence (Section 3), (2) Inclusion (Section 4), and (3) Decomposition (Section 5).Section 3 considers the existence in X of operator ranges satisfying certain conditions. The main result is the following: if X and Fare separable Banach spaces and T : Y → X is a continuous operator with nonclosed range, then there exists a nuclear operator R:Y→X such that T + R is injective and has nonclosed dense range (Theorem 3.2).Section 4 seeks to determine conditions under which every nonclosed operator range in a Banach space is contained in the range of some injective endomorphism with nonclosed dense range. Theorem 4.3 contains a sufficient condition for this. Examples of spaces satisfying this condition are c0, lp (1 < p < ∞), Lq (1 < q < 2) and their quotients. In particular, this answers a question posed by W. E. Longstaff and P. Rosenthal (Integral Equations and Operator Theory 9, (1986), 820‐830.Section 5 discusses the possibility of representing a given dense nonclosed operator range as the sum of a pair L1, L2 of operator ranges with zero intersection in the cases where (a) L1 and L2 are dense, (b) L1 and L2 are closed. The results generalize corresponding results, for endomorphisms in Hilbert space, of J. Dixmier (Bull. Soc. Math. France 77 (1949), 11‐101 and P. A. Fillmore and J. P. Williams (Adv. Math. 7 (1971), 254‐281.A final section is devoted to open problems.
Nonlinear Eigenvalue Problem for p‐Laplacian in IRN
Authors: Drábek Pavel , Rother Wolfgang 
Published: May 2007

AbstractThe nonlinear eigenvalue problem for p‐Laplacian

is considered. We assume that 1 < p < N and that the function f is of subcritical growth with respect to the variable u. The existence and C1,α‐regularity of the weak solution is proved.
On Linear Functionals of Rational Type over H(ID)
Authors: Fournier Richard 
Published: May 2007

AbstractLet H(ID) denote the set of analytic functions in the unit disk ID of the complex plane, endowed with the topology of uniform convergence on compact subsets of ID. Let Λ denote the space of continuous linear functionals over H(ID). In this paper we obtain a characterization of those λ ∈Λ such that

where B is a fixed function in H(ID). We also include a discussion of the sharpness of this characterization and an application to some extremal problem concerning Λ.
Oscillation Criteria of Comparison Type for Nonlinear Functional Differential Equations
Authors: Grace S. R. 
Published: May 2007

AbstractIn this paper we relate the oscillation problem of the nonlinear functional differential equation (a(t)x'(t))' + q(t) f (x(g(t)))= 0 and the nonlinear neutral functional differential equation (a(t) (x(t)+ p(t)x(g*(t)))'} + q(t)f (x(g(t))) = 0 to some linear second order ordinary differential equations. Recent results on linear oscillation can thus be used to obtain interesting oscillation criteria for the nonlinear equations. Similar results for the forced nonlinear functional differential equation (a(t)x'(t))' + q(t) f (x(g(t)))= e(t) and the forced neutral functional differential equation (a(t) (x(t)+ mx(t — n))')' + q(t) f (x(g(t)))= e(t) are also established. The function f appeared in the above equations is not require to be monotone.
Characterization of Compact Sets by Their Dilation Volume
Authors: Rataj Jan 
Published: May 2007

AbstractThe uniqueness up to translation of the characterization of random compact sets in Euclidean space by their dilation volumes is shown. The unique correspondence is shown to be a homeomorphism with respect to suitable topologies. If set differences of volume zero are neglected, dilations by three‐point sets are sufficient to determine a non‐random compact set and the correspondence is again a homeomorphism with respect to vague topologies.
Bi‐invariant Integrals on GL(n) with Applications
Authors: Schindler Werner 
Published: May 2007

AbstractIn this paper measures and functions on GL(n) are called bi‐invariant if they are invariant under left and right multiplication of their arguments. If v is any bi‐invariant Borel measure on GL(n), then there exists a unique Borel measure v* on D + ≥(n), the set of all diagonal matrices of rank n with positive non‐increasing diagonal entries, such that

holds for each v‐integrable bi‐invariant function f:GL(n) → IR. An explicit formula for v* will be derived in case v equals the Lebesgue measure on GL(n) and the above integral formula will be applied to concrete integration problems. In particular, if v is a probability measure, then v* can be interpreted as the distribution of the singular value vector. This fact will be used to derive a stochastic version of a theorem from perturbation theory concerning the numerical computation of the polar decomposition.
Schechter Methods of Interpolation and Commutators
Authors: Carro M. J. , Cerdà J. , Milman M. , Soria J. , Carro M. J. , Cerdà J. , Soria J. , Milman M. 
Published: May 2007

AbstractWe study the relationship between Schechter's methods of complex interpolation and the so called commutator estimates. We obtain new commutator theorems and prove characterizations of the Domain and Range spaces associated with the corresponding quasilogarithmic operator. Our methods also provide a new approach to known results, including the higher order commutator theorems for the complex method recently obtained by R. Rochberg.
Hasse‐Arf Property and Abelian Extensions
Authors: Fesenko Ivan B. 
Published: May 2007

AbstractThe paper contains discussions of relations between the property of a totally ramified p‐extension of a local field to be abelian and the property of its Galois group to possess integer jumps with respect to the upper numbering (Hasse‐Arf property). It is shown that such an extension L/F is abelian if and only if for any totally ramified abelian extension E/F the extension LE/F satisfies the Hasse‐Arf property. An additional property to the Hasse‐Arf property in terms of principal units which makes the extension abelian is established as well.
Spaces of Vector‐Valued Integrable Functions and Localization of Bounded Subsets
Authors: Florencio Miguel , Mayoral Fernando , Paúl Pedro J. 
Published: May 2007

AbstractWe study the structure of bounded sets in the space L1{E} of absolutely integrable Lusin‐measurable functions with values in a locally convex space E. The main idea is to extend the notion of property (B) of Pietsch, defined within the context of vector‐valued sequences, to spaces of vector‐valued functions. We prove that this extension, that at first sight looks more restrictive, coincides with the original property (B) for quasicomplete spaces. Then we show that when dealing with a locally convex space, property (B) provides the link to prove the equivalence between Radon–Nikodym property (the existence of a density function for certain vector measures) and the integral representation of continuous linear operators T: L1 → E, a fact well‐known for Banach spaces. We also study the relationship between Radon–Nikodym property and the characterization of the dual of L1{E} as the space L∞{E′b}.
Regularizations of Differential‐Algebraic Equations Revisited
Authors: Hanke Michael 
Published: May 2007

AbstractThe present paper deals with quasilinear differential‐algebraic equations with index 2. These equations are approximated by regularization methods. Such methods lead to singularly perturbed differential‐algebraic equations. Using a geometric theory of singular perturbations convergence of the solutions of the regularized problems towards that of the index 2 problem is proved. The limits of the present theory are discussed and directions of future research are proposed.
Decomposing Ends of Locally Finite Graphs
Authors: Jung Heinz Adolf , Niemeyer Peter 
Published: May 2007

AbstractAn important invariant of translations of infinite locally finite graphs is that of a direction as introduced by Halin. This invariant gives not much information if the translation is not a proper one. A new refined concept of directions is investigated.A double ray D of a graph X is said to be metric, if the distance metrics in D and X on V(D) are equivalent. It is called geodesic, if these metrics are equal. The translations leaving some metric double ray invariant are characterized. Using a result of Polat and Watkins, we characterize the translations leaving some geodesic double ray invariant.
The Quasiasymptotic Expansion at the Origin. Abelian‐Type Results for Laplace and Stieltjes Transforms
Authors: Nikolicacute; Danica , Pilipović Stevan 
Published: May 2007

AbstractThe notion of quasiasymptotic expansion at the origin of tempered distributions supported by [0, α] and the structural theorem for such distributions that have the quasiasymptotic expansion at the origin are given. As applications, the Abelian‐type results for the distributional Stieltjes and Laplace transforms are obtained.
The Weighted Discrepancies of Some Slowly Increasing Sequences
Authors: Ohkubo Yukio 
Published: May 2007

AbstractIn this note we give upper bounds of the weighted discrepancy of the sequence (f (n)), when f″(x) satisfies some conditions. Furthermore, by applying the generalized van der Corput's inequality, we give upper bounds of the weighted discrepancy of the sequence (f(n)), when some conditions about f (x) is satisfied, where q is any positive integer.
Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains
Authors: Parnovski L. B. 
Published: May 2007

AbstractWe investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.