Invariant functions in Denjoy–Carleman classes

Let V be a real finite dimensional representation of a compact Lie group G. It is well known that the algebra of G-invariant polynomials on V is finitely generated, say by σ ₁, . . . , σ _p . Schwarz (Topology 14:63–68, 1975) proved that each G-invariant C ^∞-function f on V has the form f = F(σ ₁, . . . , σ _p ) for a C ^∞-function F on . We investigate this representation within the framework of Denjoy–Carleman classes. One can in general not expect that f and F lie in the same Denjoy–Carleman class C ^M (with M = (M _k )). For finite groups G and (more generally) for polar representations V, we show that for each G-invariant f of class C ^M there is an F of class C ^N such that f = F(σ ₁, . . . , σ _p ), if N is strongly regular and satisfies

Ergodic Control in L∞

The infinite horizon discounted L ^∞ problem is studied as the discount factor goes to zero. It is related to the limit of the finite horizon problem as the horizon becomes infinite. The deterministic problem with and without a running cost is considered.     

Coefficient identification in the Euler–Bernoulli equation using regularization methods

In this paper, we will study the inverse problem of identification of flexural rigidity coefficient in the Euler–Bernoulli equation. This inverse problem is ill-posed. To solve it, we will use regularization methods. In particular, we will apply the mollification method and the Landweber iteration method, in particular, to find the regularized solution of the Moore–Penrose generalized inverse to a linear operator and with this, we reconstruct the coefficient. At the end of this paper, will present some examples of interest.     

D ∞-Differentials and A ∞-Structures in Spectral Sequences

We introduce the notion of D -differential and use this notion for studying the structure of differential A -algebra on multiplicative spectral sequences. We review basic notions, constructions, and results of our previous papers, where the homotopy invariance of D -differentials was proved, D -differentials and differential perturbations of chain complexes were compared, and the connection between D -differentials and differentials of multiplicative spectral sequences was established. As a consequence of this connection, we describe a method of construction of the structure of A -coalgebra on the Milnor coalgebra dual to the Steenrod algebra immediately by the differentials of the Adams spectral sequence. We describe the method of construction of the structure of A -comodule over a Milnor A -coalgebra on homologies of an arbitrary spectrum.     

Arnoldi–Tikhonov regularization methods

Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Lanczos bidiagonalization of the matrix of the given system of equations. This paper explores the possibility of instead computing a partial Arnoldi decomposition of the given matrix. Computed examples illustrate that this approach may require fewer matrix–vector product evaluations and, therefore, less arithmetic work. Moreover, the proposed range-restricted Arnoldi–Tikhonov regularization method does not require the adjoint matrix and, hence, is convenient to use for problems for which the adjoint is difficult to evaluate.     

一个加强的Carleman不等式

建立如下权系数的不等式：（1 1/m)^n≤e(1-1-2/e/m）（m=1,2,…），这里，1-2/e=0.2642411^ 为最佳值，从而得到一个加强的Carleman不等式。     

一个加强的Carleman不等式

建立如下权系数的不等式：１＋１ｍｍ≤ｅ１－１－２／ｅｍ（ｍ＝１，２，…），这里，１－２／ｅ＝０．２６４２４１１＋为最佳值．从而得到一个加强的Ｃａｒｌｅｍａｎ不等式．     

∞-Tilting Subcategories in Extriangulated Categories

In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting(resp. cotilting)subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting(resp. cotilting) subcategories and coresolving(resp. resolving) subcategories with an E-projective generator(resp. E-injective cogenerator) in an ex...     

关于Carleman位移的一点注记

的专著[1]系统地总结了含一个 Carleman 位移(或者还包含其幂次)的奇异积分方程和边值问题的理论。对于含两个 Carleman 位移的奇异积分方程和边值问题,目前已有一些研究,例如[2]、[3].就我们所见到的而论。这些研究都是在两个位移可换的假定下进行的。路见可教授请想,两个可换的 Carleman 位移之间可能有某种较强的联系,本文证实了这一猜想。由本文的结果,含两个相互可换的 Carleman 位移的奇异积     

Carleman公式的一个应用

本文从Carleman公式出发,导出了检验Riemann猜想的一个充分必要条件。     

Minimum L ∞ accelerations in Riemannian manifolds

Riemannian cubics are curves in Riemannian manifolds M that are critical points for the L ² norm of covariant acceleration, and are already rather well studied as elementary curves for interpolation problems in engineering. In the present paper the L ² norm is replaced by the L ^∞ norm, which may be more appropriate for some applications. However it is more difficult to derive the analogue of the Euler-Lagrange equation for the L ^∞ norm, requiring techniques from optimal control, and the resulting necessary conditions take a different form. These necessary conditions are examined when M is a sphere or a bi-invariant Lie group, and some examples are given.     

Radon—Nikodym Theorem in L ∞

We prove that for any given set function F which satisfies F(∪ A _i ) =sup _i F(A _i ) and F(A)=-∈fty if meas (A)=0 , there must exist a measurable function g so that F(A) = ess sup_ y ∈ A g(y) . Two proofs of this result are given. Then a Riesz representation theorem for ``linear' operators on L ^∈fty is proved and used to establish the existence of Green's function for first-order partial differential equations. In the special case u _t +H(u,Du)=0 , Green's function is explicitly found, giving the extended Lax formula for such equations. Accepted 20 March 2000. Online publication 7 July 2000.     

Carleman不等式的一种推广

本文对 Ｃａｒｌｅｍ ａｎ 不等式作出一种推广．     

Method of regularization for second-order stochastic ∗

The paper is concerned with the strong solution of secondorder stochastic evolution equations in a Hilbert space. We introduce the method of regularization to prove the existence, uniqueness of strong solution for such equations without the usual coercivity assumption. The result is applied to stochastic wave and plate equations to yield the existence of a unique strong solution for each of such problems arising from physical application.     

Thin sequences in the corona of H ∞

In this paper we consider several conditions for sequences of points in M(H ^∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $M(H^\infty )\backslash \mathbb{D}$ of H ^∞ is a thin sequence for H ^∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ^∞ necessarily satisfy the same condition.     

The L ∞-Stokes semigroup in exterior domains

The Stokes semigroup on a bounded domain is an analytic semigroup on spaces of bounded functions as was recently shown by the authors based on an a priori L ^∞-estimate for solutions to the linear Stokes equations. In this paper, we extend our approach to exterior domains and prove that the Stokes semigroup is uniquely extendable to an analytic semigroup on spaces of bounded functions.     

Carleman不等式的一种推广

本对Carlerrmn不等式作出一种推广．