共查询到20条相似文献,搜索用时 640 毫秒
1.
LetX be a Banach space and letA be the infinitesimal generator of a differentiable semigroup {T(t) |t ≥ 0}, i.e. aC
0-semigroup such thatt ↦T(t)x is differentiable on (0, ∞) for everyx εX. LetB be a bounded linear operator onX and let {S(t) |t ≥ 0} be the semigroup generated byA +B. Renardy recently gave an example which shows that {S(t) |t ≥ 0} need not be differentiable. In this paper we give a condition on the growth of ‖T′(t)‖ ast ↓ 0 which is sufficient to ensure that {S(t) |t ≥ 0} is differentiable. Moreover, we use Renardy’s example to study the optimality of our growth condition. Our results can
be summarized roughly as follows:
We also show that if lim sup
t→0+t
p ‖T′(t)‖<∞ for a givenp ε [1, ∞), then lim sup
t→0+t
p‖S′(t)‖<∞; it was known previously that if limsup
t→0+t
p‖T′(t)‖<∞, then {S(t) |t ≥ 0} is differentiable and limsup
t→0+t
2p–1‖S′(t)‖<∞. 相似文献
(i) | If lim sup t→0+t log‖T′(t)‖/log(1/2) = 0 then {S(t) |t ≥ 0} is differentiable. |
(ii) | If 0<L=lim sup t→0+t log‖T′(t)‖/log(1/2)<∞ thent ↦S(t ) is differentiable on (L, ∞) in the uniform operator topology, but need not be differentiable near zero |
(iii) | For each function α: (0, 1) → (0, ∞) with α(t)/log(1/t) → ∞ ast ↓ 0, Renardy’s example can be adjusted so that limsup t→0+t log‖T′(t)‖/α(t) = 0 andt →S(t) is nowhere differentiable on (0, ∞). |
2.
3.
John W. Snow 《Algebra Universalis》2005,54(1):65-71
A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Ln is the congruence lattice of an algebra on An for all positive integers n. Let A and B be finite algebras. We prove
Received November 11, 2004; accepted in final form November 23, 2004. 相似文献
• | If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A × B. |
• | If ConA is distributive and ConB is power-hereditary, then (ConA) × (ConB) is powerhereditary. |
• | If ConA ≅ N5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice. |
• | Every congruence lattice representation of N5 is power-hereditary. |
4.
A. S. Sivatski 《Journal of Mathematical Sciences》2007,145(1):4823-4830
The main purpose of the paper is to strengthen previous author’s results. Let k be a field of characteristic ≠ 2, n ≥ 2. Suppose
that elements
are linearly independent over ℤ/2ℤ. We construct a field extension K/k and a quaternion algebra D = (u, v) over K such that
In particular, the algebra A provides an example of an indecomposable algebra of index 2n+1 over a field, the u-invariant and the 2-cohomological dimension of which equal 2n+3 and n + 3, respectively. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 227–241. 相似文献
(1) | the field K has no proper extension of odd degree |
(2) | the u-invariant of K equals 4 |
(3) | the multiquadratic extension is not 4-excellent, and the quadratic form 〈uv,-u,-v, a〉 provides a relevant counterexample |
(4) | the central division algebra A = D ⊗E (a, t0) ⊗E (b1, t1) ⋯ ⊗E (bn, tn) does not decompose into a tensor product of two nontrivial central simple algebras over E, where E = K ((t0))((t1)) … ((tn)) is the Laurent series field in the variables t0, t1, …, tn |
(5) | ind A = 2n+1. |
5.
Let H
1, H
2 be Hilbert spaces and T be a closed linear operator defined on a dense subspace D(T) in H
1 and taking values in H
2. In this article we prove the following results:
We prove all the above results without using the spectral theorem. Also, we give examples to illustrate all the above results. 相似文献
(i) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H 1 = H 2 and T is self-adjoint, then |
(ii) | inf {‖T x‖: x ∈ D(T) ∩ N(T)⊥‖x‖ = 1} = inf {|λ|: 0 ≠ λ ∈ σ(T)} |
(iii) | Every isolated spectral value of T is an eigenvalue of T |
(iv) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T) of T |
(v) | σ(T) bounded implies T is bounded. |
6.
An interpretation is given to point interactions of the form −Δ+d inL
p
(ℝ
N
), where Δ is the Laplacian operator andd is a pseudopotential related to the ‘Dirac measure at 0', depending on the dimension. They are described as extensions of
−Δ, defined on the space {u∈C
0
∞
(ℝ
N
)|u(0)=0} that are negative generators of analytic semigroups. This is done forN=1,2 and 1<p<∞ and forN=3 and 3/2<p<3. 相似文献
7.
Jean-Christophe Bourgoin 《Calculus of Variations and Partial Differential Equations》2006,25(4):469-489
In this paper, we investigate the minimality of the map
from the Euclidean unit ball Bn to its boundary 핊n−1 for weighted energy functionals of the type Ep,f = ∫Bn f(r)‖∇ u‖p dx, where f is a non-negative function. We prove that in each of the two following cases:
Mathematics Subject Classification (2000) 58E20; 53C43 相似文献
i) | p = 1 and f is non-decreasing, |
ii) | p is integer, p ≤ n−1 and f = rα with α ≥ 0, the map minimizes Ep,f among the maps in W1,p(Bn, 핊n−1) which coincide with on ∂ Bn. We also study the case where f(r) = rα with −n+2 < α < 0 and prove that does not minimize Ep,f for α close to −n+2 and when n ≥ 6, for α close to 4−n. |
8.
Denoting Δ? the Laplacian operator on the (2N+1)-dimensional Heisenberg group ?
N
, we prove some nonexistence results for solutions of inequalities of the three types
in ?
N
and ?
N
×ℝ}+, with a∈L
∞, when 1<p≤p
0, where p
0 depends on N and the type of equation.
Received: 17 June 1999 相似文献
9.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
– | • is finitely generated and infinite-dimensional, but has only finitedimensional quotients; |
– | • has a subalgebra of finite codimension, isomorphic toM 2(k); |
– | • is prime; |
– | • has quadratic growth, and therefore Gelfand-Kirillov dimension 2; |
– | • is recursively presented; |
– | • satisfies no identity; |
– | • contains a transcendental, invertible element; |
– | • is semiprimitive if % MathType!End!2!1! has characteristic ≠2; |
– | • is graded if % MathType!End!2!1! has characteristic 2; |
– | • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!; |
– | • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!. |
10.
F. M. Mukhamedov 《Mathematical Notes》2000,67(1):81-86
In this paper an analog of the Blum-Hanson theorem for quantum quadratic processes on the von Neumann algebra is proved, i.e.,
it is established that the following conditions are equivalent:
Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 102–109, January, 2000. 相似文献
i) | P( t )x is weakly convergent tox 0; |
ii) | for any sequence {a n} of nonnegative integrable functions on [1, ∞) such that ∝ 1 ∞ a n(t)dt=1 for anyn and lim n→∞ ∥a n∥∞=0, the integral ∝ 1 ∞ a n(t)P( t )x dt is strongly convergent tox 0 inL 2(M, ϕ), wherex ɛM,P( t ) is a quantum quadratic process,M is a von Neumann algebra, andϕ is an exact normal state onM. |
11.
In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation
where
(i) r,c ∈ C([t
0, ∞), ℝ := (− ∞, ∞)) and r(t) > 0 on [t
0, ∞) for some t
0 ⩾ 0;
(ii) Φ(u) = |u|p−2
u for some fixed number p > 1.
We also generalize some results of Hille-Wintner, Leighton and Willet. 相似文献
12.
M. Rovinsky 《Selecta Mathematica, New Series》2009,15(2):343-376
Let G be the automorphism group of an extension of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we
The study of open subgroups is motivated by the study of (the stabilizers of) smooth representations undertaken in [R1, R3].
The functor Γ is an analogue of the global sections functor on the category of sheaves on a smooth proper algebraic variety.
Another result is that ‘interesting’ semilinear representations are ‘globally generated’.
相似文献
• | construct some maximal closed non-open subgroups Gv, and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G; |
• | describe, in the case of countable transcendence degree, the automorphism subgroups over the intermediate subfields (a question of Krull, [K2, §4, question 3b)]); |
• | construct, in the case n = ∞, a fully faithful subfunctor ( − )v of the forgetful functor from the category of smooth representations of G to the category of smooth representations of Gv; |
• | construct, using the functors ( − )v, a subfunctor Γ of the identity functor on , coincident (via the forgetful functor) with the functor Γ on the category of admissible semilinear representations of G constructed in [R3] in the case n = ∞ and . |
13.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
14.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
(i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
(ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
(iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
(iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
(v) | We investigate the properties of the operators from X α,p spaces to their predual. |
15.
Marie-Claude Arnaud 《Annales Henri Poincare》2008,9(5):881-926
In this article, we prove different results concerning the regularity of the C
0-Lagrangian invariant graphs of the Tonelli flows. For example :
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
• | in dimension 2 and in the autonomous generic case, we prove that such a graph is in fact C 1 on some set with (Lebesgue) full measure; |
• | under certain dynamical additional hypothesis, we prove that these graphs are C 1. |
Résumé. Dans cet article, on démontre différents résultats concernant la régularité des graphes C 0-lagrangiens invariants par des flots de Tonelli. Par exemple :
• en dimension 2, dans le cas autonome et générique, on montre que ces graphes sont de classe C 1 sur un ensemble de mesure (de Lebesque) pleine; • sous certaines hypothèses concernant la dynamique restreinte, on montre que ces graphes sont de classe C 1.
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
16.
Abstract. Let I be a finite interval, r∈ N and ρ(t)= dist {t, I} , t∈ I . Denote by Δ
s
+
L
q
the subset of all functions y∈ L
q
such that the s -difference Δ
s
τ
y(t) is nonnegative on I ,
τ>0 . Further, denote by
, 0≤α<∞ , the classes of functions x on I with the seminorm ||x
(r)
ρ
α
||_ L
p
≤ 1 , such that Δ
s
τ
x≥ 0 , τ>0 . For s=0,1,2 , we obtain two-sided estimates of the shape-preserving widths
where M
n
is the set of all linear manifolds M
n
in L
q
, such that dim M
n
≤ n , and satisfying
. 相似文献
17.
QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献
18.
Daniel Neuenschwander 《Journal of Theoretical Probability》2008,21(4):791-801
Let {μ
t
(i)}
t≥0 (i=1,2) be continuous convolution semigroups (c.c.s.) on a simply connected nilpotent Lie group G. Suppose that μ
1(1)=μ
1(2). Assume furthermore that one of the following two conditions holds:
Then μ
t
(1)=μ
t
(2) for all t≥0. As a complement, we show how our approach can be directly used to give an independent proof of Pap’s result on the uniqueness
of the embedding Gaussian semigroup on simply connected nilpotent Lie groups. In this sense, our proof for the uniqueness
of the embedding semigroup among all c.c.s. of a Gaussian measure can be formulated self-contained.
Dedicated to Professor Wilfried Hazod on the occasion of his 65th birthday. 相似文献
(i) | The c.c.s. {μ t (1)} t≥0 is a Gaussian semigroup (in the sense that its generating distribution just consists of a primitive distribution and a second-order differential operator) |
(ii) | The c.c.s. {μ t (i)} t≥0 (i=1,2) are both Poisson semigroups, and the jump measure of {μ t (1)} t≥0 is determinate (i.e., it possesses all absolute moments, and there is no other nonnegative bounded measure with the same moments). |
19.
20.
V. R. Fatalov 《Mathematical Notes》1999,65(3):358-364
In this paper we calculate the exact asymptotics of the probability P{‖w(t)+uct‖
p
>u},u→∞, wherew(t) is the standard Wiener process and ‖x‖
p
is the ordinary norm in the spaceL
p[0,1],p≥2. The result is obtained on the basis of a general theorem due to the author on the asymptotics of the Gaussian measureP(uD),u→∞, for a Borel setD belonging to a separable Banach space.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 429–436, March, 1999. 相似文献