bluuebunny/crossref_metadata_2025_split huggingface dataset:
Collocation Method for Singular Integral Equations on Holder Spaces
Authors: Schmid Ulrich 
Published: May 2007

AbstractThe classical polynomial collocation method is considered for a class of Cauchy singular integral equations with variable coefficients on a bounded interval. This method is naturally extended to the case of a non‐zero index of the underlying Fredholm operator. This is done by using the structure of the kernel and a complement of the image of this operator. For the extended method we directly obtain error bounds in the norm of the weighted Holder spaces. As an illustration, some numerical results are given.
Commutation Properties of Symmetric Operators
Authors: Trapani Camillo 
Published: May 2007

AbstractThis relationship between the weak and strong bounded commutants of a symmetric operator S and the commutant of a generalized spectral family (in Naimark's sense) of S is studied. A characterization of the existence of self‐adjoint extensions of S via von Neumann subalgebras of the weak commutant is also given.
Grothendieck Spaces of Compact Operators
Authors: Zafarani J. 
Published: May 2007

AbstractIn this paper we study the Grothendieck spaces among the operator spaces Le(E'c, F). Conditions under which Le(E'c, F) contains complemented copy of c0 are given. We apply these results to spaces of the type Cb(X; F) endowed with strict topologies.
Random Walks with Stochastically Bounded Increments: Renewal Theory
Authors: Alsmeyer Gerold 
Published: May 2007

AbstractSummary. This paper develops renewal theory for a rather general class of random walks SN including linear submartingales with positive drift. The basic assumption on SN is that their conditional increment distribution functions with respect to some filtration ℱℕ are bounded from above and below by integrable distribution functions. Under a further mean stability condition these random walks turn out to be natural candidates for satisfying Blackwell‐type renewal theorems. In a companion paper [2], certain uniform lower and upper drift bounds for SN, describing its average growth on finite remote time intervals, have been introduced and shown to be equal in case the afore‐mentioned mean stability condition holds true. With the help of these bounds we give lower and upper estimates for H * U(B), where U denotes the renewal measure of SN, H a suitable delay distribution and B a Borel subset of IR. This is then further utilized in combination with a coupling argument to prove the principal result, namely an extension of Blackwell's renewal theorem to random walks of the previous type whose conditional increment distribution additionally contain a subsequence with a common component in a certain sense. A number of examples are also presented.
A Problem in Linear Matrix Approximation
Authors: Berens H. , Finzel M. 
Published: May 2007

AbstractLet A be a normal operator in ℬ︁(H), H a complex Hilbert space, and let ℛ A = ≷ {AX ‐ XA:X ∈ ℬ︁(H)} be the commutator subspace of ℬ︁(H) associated with A. If B in ℬ︁(H) commutes with A, then B is orthogonal to ℛA with respect to the spectral norm; i.e., the null operator is an element of best approximation of B in ℛ A. This was proved by J. Anderson in 1973 and extended by P. J. Maher with respect to the Schatten p‐norm recently.We take a look at their result from a more approximation theoretical point of view in the finite dimensional setting; in particular, we characterize all elements of best approximation of B in RA and prove that the metric projection of H onto ℛA is continuous.
Hill's Equation Systems and Infinite Determinants
Authors: Denk Robert 
Published: May 2007

AbstractIn this paper a method is developed to calculate the Floquet exponents of the matrix‐valued version of Hill's equation using infinite determinants. It is shown that the Floquet exponents are precisely the zeros of an infinite determinant corresponding to the differential equation. The proof of this result uses the continuity and holomorphy of the infinite determinant.
Hilbert C*‐Modules over Monotone Complete C*‐Algebras
Authors: Frank Michael 
Published: May 2007

AbstractThe aim of the present paper is to describe self‐duality and C*‐reflexivity of Hilbert A‐modules ℳ︁ over monotone complete C*‐algebras A by the completeness of the unit ball of ℳ︁ with respect to two types of convergence being defined, and by a structural criterion. The derived results generalize earlier results ofH. Widom [Duke Math. J. 23, 309‐324, MR 17 # 1228] and W. L. Paschke [Trans. Amer. Mat. Soc. 182, 443‐468, MR 50 # 8087, Canadian J. Math. 26, 1272‐1280, MR 57 # 10433]. For Hilbert C*‐modules over commutative AW*‐algebras the equivalence of the self‐duality property and of the Kaplansky‐Hilbert property is reproved, (cf. M. Ozawa [J. Math. Soc. Japan 36, 589‐609, MR 85 # 46068]). Especially, one derives that for a C*‐algebra A the A‐valued inner product of every Hilbert A‐module ℳ︁ can be continued to an A‐valued inner product on it's A‐dual Banach A‐module ℳ︁' turning ℳ︁' to a self‐dual Hilbert A‐module if and only if A is monotone complete (or, equivalently, additively complete) generalizing a result of M. Hamana [Internat. J. Math. 3 (1992), 185 ‐ 204]. A classification of countably generated self‐dual Hilbert A‐modules over monotone complete C*‐algebras A is established. The set of all bounded module operators End′(ℳ︁) on self‐dual Hilbert A‐modules ℳ︁ over monotone complete C*‐algebras A is proved again to be a monotone complete C*‐algebra. Applying these results a Weyl‐Berg type theorem is proved.
Pointwise Multiplication of Besov and Triebel‐Lizorkin Spaces
Authors: Johnsen Jon 
Published: May 2007

AbstractIt is shown that para‐multiplication applies to a certain product π(u, v) defined for appropriate u and v in 𝒴'(IRn). Boundedness of π(.,.) is investigated for the anisotropic Besov and Triebel‐Lizorkin spaces ‐ i.e., for BM,s/p,q and FM,s/p,q with s ∈ R and p and q in [0, ∞] (though p < ∞ in the F‐case) ‐ with a treatment of the generic as well as of various borderline cases.For max (so,s,) > 0 the spaces BM,so/p,qo ⊕ BM,so/p,qo and BM,so/p,qo ⊕ BM,so/p,qo to which π(.,.) applies arc determined. For generic Bso/po,qo ⊕ Bs1/p1,q1 the receiving Fsp,q spaces are characterized.It is proved that π(f, g) = f · g holds for functions f and g when f · g ∈L1,loc, roughly speaking. In addition, π(f, u) = fu when f ∈ 𝒪M and u ∈𝒴' .Moreover, for an arbitrary open set Ω⊆ IRn, a product πΩ(., .) is defined by lifting to IRn. Boundedness of n on R′ is shown to carry over to πΩ is general.
Some Nonlinear Methods in Fréchet Operator Rings and Ψ*‐Algebras
Authors: Jung Joachim 
Published: May 2007

AbstractTwo different inverse function theorems, one of Nash‐Moser type, the other due to H. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo‐convex Fréchet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo‐convex Fréchet algebra with unit e and T+ : Ψ → Ψ a continuous linear operator. Does there exist a neighborhood U of 0 such that the equation

where T‐ = IΨ‐ T, has a solution x ∈ Ψ for every y ∈ U?
On the Values of Partial Zeta Functions of Real Quadratic Fields at Nonpositive Integers
Authors: Kallies J. , Snyder C. 
Published: May 2007

AbstractThe authors study the partial fraction decomposition of narrow class partial zeta functions of real quadratic number fields at nonpositive integer arguments and obtain an analogue of the classical v. Staudt/Clausen Theorem. The main results follow from the study of the residues ofp‐adic zeta functions associated with ray classes of modulus (p) for all rational primesp.
On the Boundedness and Compactness of Nonregular Pseudo‐Differential Operators
Authors: Marschall Jurgen 
Published: May 2007

AbstractWe study the boundedness properties of nonregular pseudo‐differential operators and their adjoints on Triebel spaces F, 0 < p, q≦ ∞. Special attention is payed to sharp estimates. The second aim of this paper is the compactness properties of these operators on weighted and unweighted Triebel spaces F(w) where the weight w may belong to an arbitrary Muckenhoupt class A∞.
On Smooth, Unramified, Étale and Flat Morphisms of Fine Logarithmic Schemes
Authors: Bauer Werner 
Published: May 2007

AbstractThe notion of unramified morphisms of schemes is generalized in a natural way to the category of fine logarithmic schemes. There are given several equivalent conditions for a morphism of fine log schemes to be unramified: vanishing of the differential module, all fibres to be unramified and a local structure theorem using charts of the log structures. In the main part of the paper there are shown some criterions for a morphism of fine log schemes to be smooth, fiat or étale in the sense of K. Kato. Letf : X → Y be a map of fine log schemes. Then f is smooth if and only if locally it can be factorized over an étale map into the standard log affine space over Y. The map f is étale if and only if it is flat and unramified. Further there are generalizations of the usual fibre criterions for flatness or smoothness of morphisms of schemes to the context of log schemes: Let f: X → Y be an S‐morphism of fine log schemes. Assume that X/S is flat and that the underlying maps of schemes are locally of finite presentation. Then f is flat if and only if the induced maps on the fibres fs : Xs → Ys, s → S, are flat. Finally f is smooth if and only if it is flat and the induced maps on the fibres f−1(y) → y,y → Y, are smooth.
On the Characterization of the Intermediate Space in Generalized Factorizations
Authors: Castro L. P. , Speck F.‐O. 
Published: May 2007

AbstractThe study of systems of singular integral equations of CAUCHYtype, of TOEPLITZand WIENER‐HOPFoperators leads to the question of existence and representation of generalized factorizations of matrix functions Φ in [LP(Γ, σ)]m. This yields a corresponding factorization of the basic multiplication or translation invariant operatorA=A_CA+, respectively, which can be seen as a splitting of a bounded into unbounded operators. The present paper is devoted to the study of the nature of the induced intermediate space Z = imA+=imA−1, in particular, for Γ = ℝ and Φ ε ζ[Cβ(ℝ)]m×mwhich is of special interest in certain applications. As we know, this implies detailed results about the structure and the explicit asymptotic behaviour of solutions of boundary and transmission problems near singular points with a relation also to eigenvalue problems which result from the classical series expansion approach or from the Mellin symbol calculus (see [13]).
The Neumann Laplacian on Generalized Ridged Domains
Authors: Edmunds David E. , Kauffman Robert M. 
Published: May 2007

AbstractWe show that for many of the bounded generalized ridged domains of Evans and Harris, all reasonable definitions of the Neumann Laplacian coincide. In particular, this shows that the lack of discreteness of the spectrum of such Laplacians is inherent, rather than an artifact of the definition.
Application of a Khintchine Inequality to Holomorphic Mappings
Authors: Floret Klaus , Matos Mário C. 
Published: May 2007

AbstractAfter proving the Khintchine inequality for the n‐Rademacher functions of ARON and GLOBVENIK with constants independent from n ε IN, applications are given to the theory of polynomials and holomorphic functions between Banach spaces. In particular, the following result is proved: Every entire mapping from a Banach space into another one of cotype q, vanishing at the origin and of r‐dominated type at zero for some r > 0 maps unconditionally 2‐summable sequences into absolutely q‐summable sequences.
Lamé Potentials and the Stationary (m)KdV Hierarchy
Authors: Gesztesy F. , Weikard R. 
Published: May 2007

AbstractA new method of constructing elliptic finite‐gap solutions of the stationary Korteweg‐de Vries (KdV) hierarchy, based on a theorem due to PICARD, is illustrated in the concrete case of the Lamé‐Ince potentials ‐s(s + 1) ρ(z), sε (ρ(.) the elliptic Weierstrass function). Analogous results are derived in the context of the stationary modified Korteweg‐de Vries (mKd V) hierarchy for the first time.
Pontryagin Duality for a Class of Locally Compact Quantum Groups
Authors: Hollevoet Jan 
Published: May 2007

AbstractA class of locally compact quantum semigroups in the sense of WORONOWICZ, containing the quantized Heisenberg group, is studied. The underlying quantum space is described in terms of a crossed product. We show the existence of a universal corepresentation and a Pontryagin dual, which turns out to be a twisted crossed product. The Pontryagin duality for these quantum semigroups is investigated.
On Scales of Summability Methods
Authors: Kiesel Rüdiger 
Published: May 2007

AbstractIn this paper we consider generalized Nörlund methods (Nαp), α > ‐1, power series methods (Jp) and the iteration product of two such methods. A particular case is that of the Cesaro means (Cα) with corresponding power series method (A), i.e., Abel's method. We obtain generalizations of inclusion, and tauberian and convexity theorems which are well‐known for the Cesàro‐Abel case, for a rich class of methods of the above type.
Nonexistence of Global Solutions of Some Quasilinear Hyperbolic Equations with Dynamic Boundary Conditions
Authors: Kirane M. , Kouachi S. , Tatar N. 
Published: May 2007

AbstractIn this paper the non‐existence of global solutions of two fourth‐order hyperbolic equations with dynamic boundary conditions is considered. The method of proof makes use of the generalized convexity method due to Ladyzhenskaya and Kalantarov [4].
Representation of Generalized Fractional Integrals in Terms of Laplace Transforms on Spaces Lp
Authors: Kiryakova Virginia , Raina R. K. , Saigo Megumi 
Published: May 2007

AbstractIn this paper the generalized fractional integration operators defined by Kiryakova [6], [7] are expressed in terms of the Laplace transform L and its inverse L−1. These decomposition results are established on Lp spaces and some examples are deduced as their special cases.
Some Special Tauberian Theorems for Fourier Type Integrals and Eigenfunction Expansions of Sturm‐Liouville Equations on the Whole Line
Authors: Levitan B. M. 
Published: May 2007

AbstractWe offer a new proof of a special Tauberian theorem for Fourier type integrals. This Tauberian theorem was already considered by us in the papers [1] and [2]. The idea of our initial proof was simple, but the details were complicated because we used Bochner's definition of generalized Fourier transform for functions of polynomial growth. In the present paper we work with L. Schwartz's generalization. This leads to significant simplification. The paper consists of six sections. In Section 1 we establish an integral representation of functions of polynomial growth (subjected to some Tauberian conditions), in Section 2 we prove our main Tauberian theorems (Theorems 2.1 and 2.2.), using the integral representation of Section 1, in Section 3 we study the asymptotic behavior of M. Riesz's means of functions of polynomial growth, in Sections 4 and 5 we apply our Tauberian theorems to the problem of equiconvergence of eigenfunction expansions of Sturm‐Liouville equations and expansion in ordinary Fourier integrals, and in Section 6 we compare our general equiconvergence theorems of Sections 4 and 5 with the well known theorems on eigenfunction expansions in classical orthogonal polynomials. In some sense this paper is a re‐made survey of our results obtained during the period 1953‐58. Another proof of our Tauberian theorem and some generalization can be found in the papers [3] and [4].
The Poisson Voronoi Tessellation I. A Basic Identity
Authors: Mecke Joseph , Muche Lutz 
Published: May 2007

AbstractThis paper gives basic relations between the stationary Poisson point process and the point process of vertices of the corresponding Voronoi tessellation in IRdand of planar sections through it. The results are based on a study of the Palm distribution of the point process of vertices. An identity is given connecting the distribution of a Poisson point process and the Palm distribution with respect to the vertices of the corresponding Voronoi tessellation. Distributional properties for the edges are discussed. Finally, identities are given for characteristics of the “typical” edge and an edge chosen at random emanating from the “typical” vertex.
Inner Derivations on σ‐C*‐Algebras
Authors: Christopher Phillips N. 
Published: May 2007

AbstractWe prove the following two improvements of a result of Becker. (1) If A is a pro‐C*‐algebra, then every derivation on A is approximately inner. (2) If A is a separable σ‐C*‐algebra, and if every C* quotient of A has the property that every derivation on it is inner, then also every derivation on A is inner. We also give an example of a derivation on a separable σ‐C*‐algebra which is not inner but which induces an inner derivation on every C* quotient.
Validity and Limitation of the Newell‐Whitehead Equation
Authors: Schneider Guido 
Published: May 2007

AbstractModulation equations play an essential role in the description of systems which exhibit patterns of nearly periodic nature, e.g. in Bénard's problem. The so called Newell‐Whithead equation is derived to describe the envelope of modulated roll‐solutions in systems with two large extended or unbounded space directions. Here the validity question for the Newell‐Whitehead equation is treated, i.e., estimates between the exact solutions of the original problem and the associated approximations are given. The Newell‐Whitehead equation is a good example how important this validity question is. Although the modulation equation can formally be derived, the solutions of the original system can behave in some situations in a completely different manner than predicted by the modulation equation. This happens on a time scale which is very small compared to the natural one.
Linearized Oscillations for Differential Equations of Neutral Type
Authors: Shen Jianhua 
Published: May 2007

AbstractAbstract.Consider the nonlinear neutral delay differential equationmagnified imagewithP(t),Q(t) continuous, τ > 0, σ> 0. We obtain new sufficient conditions for the oscillation of all solutions by an associate linear equation, and thereby establish some new criteria as proposed in an earlier open problem.
Vector Fields as Derivations on Nuclear Manifolds
Authors: Thomas E. G. F. 
Published: May 2007

AbstractIf M is a manifold modelled over a nuclear Fréchet space, the smooth vector fields, as in the finite dimensional case, may be identified with continuous derivations in the space ζ(M) of real C∞ functions on M. This applies for instance to the loop groups and the group of diffeomorphisms of the circle: M = ζ(S1, G), M = Diff(S1).
A Note on the Galerkin Method's Stability
Authors: Titensky M. E. 
Published: May 2007

AbstractNumerical stability of the Galerkin method for some class of semilinear evolution equations is studied. The stability is established in thelp(1 <p < ∞) norms. Our results are applied to the special coordinate systems. All the conditions of the stability theorems proved in this note may be readily verifiable in practice for them.
Supersoluble and Related Cofinitary Groups
Authors: Wehrfritz B. A. F. 
Published: May 2007

AbstractLet D be a division ring (possibly commutative) and V an infinite‐dimensional left vector space over D. We consider irreducible subgroups G of GL(V) containing an element whose fixed‐point set in V is non‐zero but finite dimensional (over D). We then derive conclusions about cofinitary groups, an element of GL(V) being cofinitary if its fixed‐point set is finite dimensional and a subgroup G of GL(V) being cofinitary if all its non‐identity elements are confinitary. In particular we show that an irreducible cofinitary subgroup G of GL(V) is usually imprimitive if G is supersoluble and is frequently imprimitive if G is hypercyclic. The latter includes the case where G is hypercentral, which apparently is also new.
Cwikel Type Estimates in Non‐Power Ideals
Authors: Weidl Timo 
Published: May 2007

AbstractThe Cwikel inequality for integral operators of the type a(x)b(D) will be generalized. It will be shown that the asymptotical behavior of the singular numbers of such operators in general can be estimated by the asymptotics of classical phase space volume spanned by these symbols. Applications to non‐power symbols are given.
Saint Venant's Principle in Statical and Dynamical Problems for an Elastic Wedge and a Cone
Authors: Budaev B. V. , Morozov N. F. , Narbut M. A. 
Published: May 2007

AbstractThe boundary problems for an elastic wedge and a cone in statics and dynamics are investigated with special emphasis on Saint Venant's principle. The exact analytical solutions are obtained by integral transform technique and the far‐field asymptotics is obtained.
Some Properties of Minimal Splines
Authors: Demjanovich Yu. K. 
Published: May 2007

AbstractS. G. Mikhlin was the first to construct systematically coordinate functions on an equidistant grid solving a system of approximate equations (called “fundamental relations”, see [5]; Goel discussed some special cases earlier in 1969; see also [1, 4, 6]). Further, the idea was developed in the case of irregular grids (which may have finite accumulation points, see [1] ).This paper is devoted to the investigation of A‐minimal splines, introduced by the author; they include polynomial minimal splines which have been discussed earlier. Using the idea mentioned above, we give necessary and sufficient conditions for existence, uniqueness and g‐continuity of these splines. The application of these results to polynomial splines of m‐th degree on an equidistant grid leads us, in particular, to necessary and sufficient conditions for the continuity of their i‐th derivative (i = 1, ⃛, m). These conditions do not exclude discontinuities of other derivatives (e.g. of order less than i). This allows us to give a certain classification of minimal spline spaces. It turns out that the spline classes are in one‐to‐one‐correspondence with certain planes contained in a hyperplane.
The Qualocation Method for Symm's Integral Equation on a Polygon
Authors: Elschner J. , Prössdorf S. , Sloan I. H. 
Published: May 2007

AbstractThis paper discusses the convergence of the qualocation method for Symm's integral equation on closed polygonal boundaries in IR2. Qualocation is a Petrov‐Galerkin method in which the outer integrals are performed numerically by special quadrature rules. Before discretisation a nonlinear parametrisation of the polygon is introduced which varies more slowly than arc‐length near each corner and leads to a transformed integral equation with a regular solution. We prove that the qualocation method using smoothest splines of any order k on a uniform mesh (with respect to the new parameter) converges with optimal order O (hk). Furthermore, the method is shown to produce superconvergent approximations to linear functionals, retaining the same high convergence rates as in the case of a smooth curve.
Nonlinear programming the choice of direction by gradient projection
Authors: Zwart Philip B. 
Published: May 2007

AbstractRosen's method of Gradient Projection chooses a search direction which is not necessarily the direction of steepest ascent. However, the projection of the gradient onto a “suitably chosen subspace” does yield the direction of steepest ascent. The suitable choice is easily recognized as a result of some theorems relating gradient projection to steepest ascent. These results lead to a modification of Rosen's method. The modification improves the choice of search direction and usually yields the steepest ascent direction without solving a quadratic programming problem.