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1.
Suppose A generates a strongly continuous linear group on a Banach space X and B is a linear operator on X. It is shown that an extension of generates a strongly continuous semigroup if and only if the family of operators has an appropriate evolution system. This produces simple sufficient conditions for an extension of to generate a strongly continuous semigroup, including
(1)  being m-dissipative and for all x in the domain of B; or
(2)  being m-dissipative and being a commuting family of operators with
dense. This is applied to many differential operators; for at least one class of applications, the semigroup is generated by the closure of and the equivalence between semigroups and evolution systems enables us to construct it explicitly. In all the applications, including the sufficient conditions (1) and (2) above, the semigroup generated by an extension of is given by the Trotter product formula
  相似文献   

2.
We consider Hilbert spaces of analytic functions defined on an open subset of , stable under the operator Mu of multiplication by some function u. Given a subspace of which is nearly invariant under division by u, we provide a factorization linking each element of to elements of on the inverse image under u of a certain complex disc, for which we give a relatively simple formula. By applying these results to and u(z) = z, we obtain interesting results involving a H2-norm control. In particular, we deduce a factorization for the kernel of Toeplitz operators on Dirichlet spaces. Finally, we give a localization for the problem of extraneous zeros.Submitted: January 18, 2003 Revised: December 20, 2003  相似文献   

3.
In this paper, we consider global solutions for the following nonlinear Schrödinger equation in with and We show that no nontrivial solution can decay faster than the solutions of the free Schrödinger equation, provided that u(0) lies in the weighted Sobolev space in the energy space, namely or in according to the different cases.  相似文献   

4.
We discuss the partial regularity of minimizers of energy functionals such as
where u is a map from a domain into the m-dimensional unit sphere of and A is a differential one-form in .  相似文献   

5.
Let be a partially ordered set, Int the system of all (nonempty) intervals of partially ordered by the set-theoretical inclusion . We are interested in partially ordered sets with Int isomorphic to Int . We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If is a directed partially ordered set, the only with Int isomorphic to Int are corresponding to direct decompositions of ( denotes the dual of . The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11].  相似文献   

6.
Let L(x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H(xp) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution of the Hamilton-Jacobi equation
is an action function in the large, i.e.,
for all Received: 13 June 2003  相似文献   

7.
In this paper, we give an Lp-Lq-version of Morgans theorem for the Dunkl-Bessel transform on More precisely, we prove that for all and then for all measurable function f on the conditions and imply f = 0, if and only if where are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004  相似文献   

8.
It is well known that imprimitive P-polynomial association schemes with are either bipartite or antipodal, i.e., intersection numbers satisfy either for all for all . In this paper, we show that imprimitive -polynomial association schemes with are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either .  相似文献   

9.
10.
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form . A criterion is given determining whether a cyclic variety is interpretable in . For a permutation without fixed elements, it is stated that a set of primes for which is interpretable in in the lattice is finite. It is also proved that for distinct primes , the Helly number of a type in coincides with dimension of the dual type and equals .  相似文献   

11.
For a discrete group G, we prove that a G-map between proper GCW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K * G (E(G, in)), is isomorphic to K * G (E(G, )), where E(G, ) denotes the classifying space for the family of finite cyclic subgroups of G. Letting be the family of virtually cyclic subgroups of G, we also establish that and related results.  相似文献   

12.
We study the asymptotic behavior as of the Sobolev norm of the solution to the Cauchy problem for the one-dimensional quasilinear Burgers type equation (It is assumed that the problem is , the boundary conditions are periodic, and .) We show that the locally time-averaged Sobolev norms satisfy the estimate . The estimates obtained as a consequence for the Fourier coefficients justify Kolmogorov's spectral theory of turbulence for the case of the Burgers equation.  相似文献   

13.
A singular rank one perturbation of a self-adjoint operator A in a Hilbert space is considered, where and but with the usual A–scale of Hilbert spaces. A modified version of the Aronszajn-Krein formula is given. It has the form where F denotes the regularized Borel transform of the scalar spectral measure of A associated with . Using this formula we develop a variant of the well known Aronszajn–Donoghue spectral theory for a general rank one perturbation of the class.Submitted: March 14, 2002 Revised: December 15, 2002  相似文献   

14.
Consider a path-integral which is the solution to a diffusion version of the generalized Schro¨dinger's equation . Here , where A is an infinitesimal generator of a strongly continuous Markov Semigroup corresponding to the diffusion process . For and V replaced by one obtains , which represents a quantum mechanical Hamiltonian corresponding to a particle of mass 1 (in atomic units) subject to interaction with potential V. This paper is concerned with computer calculations of the second eigenvalue of by generating a large number of trajectories of an ergodic diffusion process.  相似文献   

15.
Bakhvalov  A. N. 《Mathematical Notes》2002,72(3-4):454-465
In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called -convergent if the limit of rectangular partial sums over all indices for which for all j and k exists. In the space of arbitrary even dimension 2m we construct an example of a continuous function with an estimate of the modulus of continuity such that its Fourier series is -divergent everywhere for any .  相似文献   

16.
We characterize the group Aut for the symmetrized bidisc
Both authors were supported in part by KBN grant no. 5 P03A 033 21 and by DFG grant no. 227/8-1.  相似文献   

17.
18.
Griniv  R. O.  Shkalikov  A. A. 《Mathematical Notes》2003,73(5-6):618-624
In this paper, we consider equations of the form , where is a function with values in the Hilbert space , the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in . The linear operator generating the C 0-semigroup in the energy space is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms.  相似文献   

19.
In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.  相似文献   

20.
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