Grand Bochner–Lebesgue space and its associate space

Our aim is to introduce the grand Bochner–Lebesgue space in the spirit of Iwaniec–Sbordone spaces, also known as grand Lebesgue spaces, and prove some of its properties. We will also deal with the associate space for grand Bochner–Lebesgue spaces.     

Geodesic discs in Teichmiiller space

Let T(S) be the Teichmuller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincare disc into T(S). It is shown in this paper that for any non-Strebel point τ∈T(S), there are infinitely many aeodesic discs containina [0] and τ.     

A Kre?n space coordinate free version of the de Branges complementary space

Let Z be a maximal nonnegative subspace of a Kre?n space X, and let X/Z be the quotient of X modulo Z. Define

H(Z)={h∈X/Z|sup{−X[x,x]|x∈h}<∞}.     

A quantum Teichmüller space

We explicitly describe a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes that is equivariant with respect to the action of the mapping class group. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 3, pp. 511–528, September, 1999.     

Special standard static space–times

Essentially, some conditions for the Riemannian factor and the warping function of a standard static space–time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space–time Einstein.     

Gδ-embeddings in Hilbert space

It is shown that a separable Banach space X has the point of weak to norm continuity property (resp. the Radon-Nikodym property) if and only if there exists a compact G_δ-embedding (resp. an H^δ-embedding) from X into l₂. This solves several questions of J. Bourgain and H. P. Rosenthal (J. Funct. Anal.52 (1983)). It is also shown that every non-relatively compact sequence in a Banach space with property (PC) has a difference subsequence which is a boundedly complete basic sequence. This solves a question of Pelczynski and extends some results of W. B. Johnson and H. P. Rosenthal (Studia Math.43 (1972), 77–92). Various related questions asked in the above Bourgain-Rosenthal reference and by G. A. Edgar and R. F. Wheeler (Pac. J. Math.115 (1984)) and N. Ghoussoub and H. P. Rosenthal (Math. Ann.264 (1983), 321–332) are also settled.     

On immersions ofn-dimensional Lobachevskií space in 2n-dimensional Euclidean space withn principal direction fields

In this article we prove that the principal direction fields are holonomic and use them to introduce curvilinear coordinates on an immersed region in terms of which the linear element of Lobachevskií space is written in the form where The fundamental system of equations is established for an immersion ofn-dimensional Lobachevskií space into 2n-dimensional Euclidean space withn principal direction fields for the functions _i and, and a way of constructing an arbitrary local analytic immersion is shown.Translated from Ukrainskií Geometricheskií Sbornik, No. 28, pp. 3–8, 1985.     

Cylindrically symmetric gravitational-wavelike space–times

We present Noether symmetries of a geodetic Lagrangian for a time-conformal cylindrically symmetric space–time. We introduce a time-conformal factor in the general cylindrically symmetric space–time to make it nonstatic and then find approximate Noether symmetries of the action of the corresponding Lagrangian. Taking the perturbation up to the first order, we find all Lagrangians for cylindrically symmetric space–times for which approximate Noether symmetries exist.     

Geodesic discs in teichmüller space

LetT(S) be the Teichmüller space of a Riemann surfaceS. By definition, a geodesic disc inT(S) is the image of an isometric embedding of the Poincaré disc intoT(S). It is shown in this paper that for any non-Strebel pointτ ∈ T(S), there are infinitely many geodesic discs containing [0] and τ.     

Does Boris-SDC conserve phase space volume?

In this paper we investigate the conservation of phase space volume of the Boris-SDC algorithm. This method provides a generic way to extend the standard, second-order accurate Lorentz force integrator commonly used for charged particles in an electric and magnetic field to a high-order method using spectral deferred corrections. For a single particle in a Penning trap and different frequencies of the electric and magnetic fields, we assess the conservation properties of the method by computing the update matrix of one step of Boris-SDC as well as its determinant. We compare the results to the convergence regions and relate them to energy conservation properties of the method. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamical sampling: Time–space trade-off

We consider the problem of spatiotemporal sampling in which an initial state of an evolution process is to be recovered from a set of samples at different time levels. We are particularly interested in lossless trade-off between spatial and temporal samples. We show that for a special class of signals it is possible to recover the initial state using a reduced number of measuring devices activated more frequently. We present several algorithms for this kind of recovery and describe their robustness to noise.     

Smoothing algorithms for state–space models

Two-filter smoothing is a principled approach for performing optimal smoothing in non-linear non-Gaussian state–space models where the smoothing distributions are computed through the combination of ‘forward’ and ‘backward’ time filters. The ‘forward’ filter is the standard Bayesian filter but the ‘backward’ filter, generally referred to as the backward information filter, is not a probability measure on the space of the hidden Markov process. In cases where the backward information filter can be computed in closed form, this technical point is not important. However, for general state–space models where there is no closed form expression, this prohibits the use of flexible numerical techniques such as Sequential Monte Carlo (SMC) to approximate the two-filter smoothing formula. We propose here a generalised two-filter smoothing formula which only requires approximating probability distributions and applies to any state–space model, removing the need to make restrictive assumptions used in previous approaches to this problem. SMC algorithms are developed to implement this generalised recursion and we illustrate their performance on various problems.     

A characterization of λ-central BMO space

We give a characterization of the λ-central BMO space via the boundedness of commutators of n-dimensional Hardy operators.     

μ-average N-widths on the Wiener space

In this paper we investigate the asymptotic behaviour of μ-averagen-widths of integral operatorK on the Wiener space, whereK is the inverse operator of an ordinary linear differential operatorL of orderm. For 1≤p.q<∞ . and forp∈[1, ∞),q∈[2, ∞) . Supported by the Fund. of Dooctoral program of NECC.     

A Kähler structure on the moduli space of isometric maps of a circle into Euclidean space

We study the spaces and and _Lip of smooth (resp. non-degenerate Lipschitz) isometric maps of a circle into Euclidean space modulo orientation preserving Euclidean motions. We prove that and _Lip are infinite dimensional Kähler manifolds. In particular, they are complex Fréchet (resp. Banach) manifolds. This is proved by an infinite dimensional version of the Kirwan, Kempf-Ness Theorem [Kir84], [KN78], [Nes84] relating symplectic quotients to holomorphic quotients, applied to the action ofPSL ₂() on the free loop space ofS ².Oblatum 15-X-1994 & 5-VII-1995This research was supported in part by NSF grant DMS-92-05154.This research was partially supported by AFOSR grant F49620-92-J-0093.     

Quantization of the universal Teichmüller space

In the first part of the paper, we describe the Kähler geometry of the universal Teichmüller space, which can be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The universal Teichmüller space contains classical Teichmüller spaces T(G), where G is a Fuchsian group, as complex submanifolds. The quotient Diff₊(S ¹)/Möb(S ¹) of the diffeomorphism group of the unit circle modulo Möbius transformations can be considered as a “smooth” part of the universal Teichmüller space. In the second part we describe how to quantize Diff₊(S ¹)/Möb(S ¹) by embedding it in an infinite-dimensional Siegel disc. This quantization method does not apply to the whole universal Teichmüller space. However, this space can be quantized using the “quantized calculus” of A. Connes and D. Sullivan.     

A new coordinate of teichmüller space

By using the theory of quadratic differentials, we give a new coordinate to the Teichmüller space as well as the trajectory structures of a special class of Jenkins-Strebel quadratic differentials.