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1.
《Mathematische Nachrichten》2018,291(1):41-54
We show that nontrivial convolution operators on certain spaces of entire functions on E are frequently hypercyclic when E is a normed space and when E is the strong dual of a Fréchet nuclear space. We also obtain results of existence and approximation for convolution equations on certain spaces of entire functions on arbitrary locally convex spaces. 相似文献
2.
Given two Banach spaces E,F, let B(E,F) be the set of all bounded linear operators from E into F, Σ
r
the set of all operators of finite rank r in B(E,F), and Σ
r
# the number of path connected components of Σ
r
. It is known that Σ
r
is a smooth Banach submanifold in B(E,F) with given expression of its tangent space at each A ∈ Σ
r
. In this paper,the equality Σ
r
# = 1 is proved. Consequently, the following theorem is obtained: for any nonnegative integer r, Σ
r
is a smooth and path connected Banach submanifold in B(E,F) with the tangent space T
A
Σ
r
= {B ∈ B(E,F): BN(A) ⊂ R(A)} at each A ∈ Σ
r
if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property
of Σ
r
the method presented in this paper is also interesting. As an application of this result, it is proved that if E = ℝ
n
and F = ℝ
m
, then Σ
r
is a smooth and path connected submanifold of B(ℝ
n
, ℝ
m
) and its dimension is dimΣ
r
= (m+n)r−r
2 for each r, 0 <- r < min {n,m}.
Supported by the National Science Foundation of China (Grant No.10671049 and 10771101). 相似文献
3.
We define and investigateCD
Σ,Γ(K, E)-type spaces, which generalizeCD
0-type Banach lattices introduced in [1]. We state that the space CD
Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8]. 相似文献
4.
In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL
α
1
(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those
which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range.
Supported by NNSFC No.19671036 相似文献
5.
Given an elliptic curve Σ, flat E
k
-bundles over Σ are in one-to-one correspondence with smooth del Pezzo surfaces of degree 9 − k containing Σ as an anti-canonical curve. This correspondence was generalized to Lie groups of any type. In this article,
we show that there is a similar correspondence between del Pezzo surfaces of degree 0 with an A
d
-singularity containing Σ as an anti-canonical curve and Kac–Moody [(E)\tilde]k{\widetilde{E}_{k}}-bundles over Σ with k = 8 − d. In the degenerate case where surfaces are rational elliptic surfaces, the corresponding [(E)\tilde]k{\widetilde{E}_k}-bundles over Σ can be reduced to E
k
-bundles. 相似文献
6.
Veil B. SHAKHMUROV 《数学学报(英文版)》2006,22(5):1493-1508
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators D^α from this space to Eα-valued Lp,γ spaces is proved. These results are applied to partial differential-operator equations with parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters. 相似文献
7.
Anton D. Baranov 《Arkiv f?r Matematik》2006,44(1):16-38
We study the problem of density of polynomials in the de Branges spaces ℋ(E) of entire functions and obtain conditions (in terms of the distribution of the zeros of the generating function E) ensuring that the polynomials belong to the space ℋ(E) or are dense in this space. We discuss the relation of these results with the recent paper of V. P. Havin and J. Mashreghi
on majorants for the shift-coinvariant subspaces. Also, it is shown that the density of polynomials implies the hypercyclicity
of translation operators in ℋ(E). 相似文献
8.
Donald I. Cartwright 《Monatshefte für Mathematik》2001,247(1):93-109
To any locally finite thick building of type there is naturally associated a commutative algebra of operators. When is constructed from a local field F with local ring , and , then is isomorphic to the convolution algebra of compactly supported bi-K-invariant functions on PGL(n+1,F). We give a proof, valid for any , that the multiplicative functionals on may all be expressed in terms of Hall–Littlewood polynomials. Regarding as a subalgebra of the C *-algebra of bounded operators on the space of square summable functions on the vertex set of , we find the spectrum of the C *-algebra , the closure of . This generalizes results obtained in [3] when n = 1 and in [5] when n = 2. 相似文献
9.
We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on Hb(V), V absolutely convex open set. 相似文献
10.
Donald I. Cartwright 《Monatshefte für Mathematik》2001,133(2):93-109
To any locally finite thick building of type there is naturally associated a commutative algebra of operators. When is constructed from a local field F with local ring , and , then is isomorphic to the convolution algebra of compactly supported bi-K-invariant functions on PGL(n+1,F). We give a proof, valid for any , that the multiplicative functionals on may all be expressed in terms of Hall–Littlewood polynomials. Regarding as a subalgebra of the C
*-algebra of bounded operators on the space of square summable functions on the vertex set of , we find the spectrum of the C
*-algebra , the closure of . This generalizes results obtained in [3] when n = 1 and in [5] when n = 2.
(Received 26 June 2000; in revised form 21 February 2001) 相似文献
11.
Alan Robinson 《Inventiones Mathematicae》2003,152(2):331-348
We prove that the stable homotopy of any Γ-module F is the homology of a bicomplex Ξ(F), in which the (q−1)st row is the two-sided bar construction ℬ(Lie*
q
,Σ
q
,F[q]). This gives a natural homotopical cotangent bicomplex for graded commutative algebras, in a form suitable for use in a
new obstruction theory for classifying E
∞ ring structures on spectra. The E
∞ structure on certain Lubin-Tate spectra is a corollary.
Oblatum 15-X-2001 & 14-X-2002?Published online: 24 February 2003 相似文献
12.
Ji-pu Ma Tseng Yaun Rong Functional Analysis Research Center Harbin Normal University Harbin China 《中国科学A辑(英文版)》2007,50(9):1233-1239
Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. < ∞ or codim R(T) = const.< ∞} and {T ∈ R(E, F) RankT =const.<∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry. 相似文献
13.
Liliana Gabriela Gheorghe 《Annali di Matematica Pura ed Applicata》2001,180(2):203-210
We study membership to Schatten ideals S
E
, associated with a monotone Riesz–Fischer space E, for the Hankel operators H
f
defined on the Hardy space H
2(∂D). The conditions are expressed in terms of regularity of its symbol: we prove that H
f
∈S
E
if and only if f∈B
E
, the Besov space associated with a monotone Riesz–Fischer space E(dλ) over the measure space (D,dλ) and the main tool is the interpolation of operators.
Received: December 17, 1999; in final form: September 25, 2000?Published online: July 13, 2001 相似文献
14.
Richard A. Alò Andrè de Korvin Charles Roberts 《Annali di Matematica Pura ed Applicata》1977,112(1):33-48
Summary Under study is the existence of averaging operators determined by measurable maps φ from a measure space (S, Σ, μ) into an
arbitrary Hausdorff topological space T. The map φ induces a continuous map φe from the space Cb(T) into the normed (Banach) function space Lϱ = Lϱ(S, Σ, μ) defined by φe(f)=foφ for all f ε Cb(T). An integral representation for such operators is first studied. The existence is then determined by the existence of
an averaging operator U1 for the restriction of φ to a certain measurable subset B1 of S. Utilizing a representation of Lϱ(S, Σ, μ) as a Banach function space over a compact extremally disconnected Hausdorff space Ŝ, we are able to give a definition
for the concept of plural points and irreducible map. A significant upper bound is given for the operator U1. Finally conditions are considered under which no bounded projection from Lϱ onto the range of φe may exist. From a topological point of view the development is pursued in a general setting. Averaging operators have recently
been used for the study of injective Banach spaces of the type Cb(T) and in non-linear prediction and approximation theory relative to Tshebyshev subspaces of Lϱ.
Entrata in Redazione l’ll settembre 1975. 相似文献
15.
V. V. Arestov 《Mathematical Notes》1998,64(3):279-294
We study the relationship between several extremum problems for unbounded linear operators of convolution type in the spaces
, m ≥ 1, 1 ≤ γ ≤ ∞. For the problem of calculating the modulus of continuity of the convolution operatorA on the function classQ defined by a similar operator and for the Stechkin problem on the best approximation of the operatorA on the classQ by bounded linear operators, we construct dual problems in dual spaces, which are the problems on, respectively, the best
and the worst approximation to a class of functions by another class.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 323–340, September, 1998.
This research was supported by INTAS under grant No. 94-4070. 相似文献
16.
17.
Yu. G. Shondin 《Mathematical Notes》1999,66(6):764-776
In the paper we study supersymmetric models for point interaction perturbations of operators of Dirac type and their spectral
properties. Such models are considered in the class of odd self-adjoint operators in ℤ2-graded Pontryagin space. We present in detail the previously considered realization method of strongly singular perturbation
by means of their embedding into the theory of self-adjoint extensions. We describe odd self-adjoint extensions of odd symmetric
operators with deficiency indices (1,1) in ℤ2-graded Pontryagin space and squares of such extensions using Krein’s formula for the resolvent. The results obtained are
refined in application to singular perturbations of odd self-adjoint differential operators.
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 924–940, December, 1999. 相似文献
18.
19.
Suppose that E and F are two Banach spaces and that B(E, F) is the space of all bounded linear operators from E to F. Let T
0∈B(E, F) with a generalized inverse T
0
+∈B(F, E). This paper shows that, for every T∈B(E, F) with ‖T
0
+ (T−T
0)‖<1, B ≡ (I + T
0
+(T−T
0))−1
T
0
+ is a generalized inverse of T if and only if (I−T
0
+
T
0)N(T) = N(T
0), where N(·) stands for the null space of the operator inside the parenthesis. This result improves a useful theorem of Nashed and
Cheng and further shows that a lemma given by Nashed and Cheng is valid in the case where T
0 is a semi-Fredholm operator but not in general. 相似文献
20.
Sanming Zhou 《Annals of Combinatorics》2010,14(3):397-405
A connected graph Σ of girth at least four is called a near n-gonal graph with respect to E, where n ≥ 4 is an integer, if E is a set of n-cycles of Σ such that every path of length two is contained in a unique member of E. It is well known that connected trivalent symmetric graphs can be classified into seven types. In this note we prove that
every connected trivalent G-symmetric graph S 1 K4{\Sigma \neq K_4} of type G12{G^1_2} is a near polygonal graph with respect to two G-orbits on cycles of Σ. Moreover, we give an algorithm for constructing the unique cycle in each of these G-orbits containing a given path of length two. 相似文献