共查询到20条相似文献,搜索用时 34 毫秒
1.
Goro Akagi 《Journal of Evolution Equations》2011,11(1):1-41
Let V and V* be a real reflexive Banach space and its dual space, respectively. This paper is devoted to the abstract Cauchy problem
for doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations of the form:
?V yt (u¢(t)) + ?V j(u(t)) + B(t, u(t)) ' f(t){\partial_V \psi^t (u{^\prime}(t)) + \partial_V \varphi(u(t)) + B(t, u(t)) \ni f(t)} in V*, 0 < t < T, u(0) = u
0, where ?V yt, ?V j: V ? 2V*{\partial_V \psi^t, \partial_V \varphi : V \to 2^{V^*}} denote the subdifferential operators of proper, lower semicontinuous and convex functions yt, j: V ? (-¥, +¥]{\psi^t, \varphi : V \to (-\infty, +\infty]}, respectively, for each t ? [0,T]{t \in [0,T]}, and f : (0, T) → V* and u0 ? V{u_0 \in V} are given data. Moreover, let B be a (possibly) multi-valued operator from (0, T) × V into V*. We present sufficient conditions for the local (in time) existence of strong solutions to the Cauchy problem as well as
for the global existence. Our framework can cover evolution equations whose solutions might blow up in finite time and whose
unperturbed equations (i.e., B o 0{B \equiv 0}) might not be uniquely solved in a doubly nonlinear setting. Our proof relies on a couple of approximations for the equation
and a fixed point argument with a multi-valued mapping. Moreover, the preceding abstract theory is applied to doubly nonlinear
parabolic equations. 相似文献
2.
The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions
Olli Hyv?rinen Mika Kemppainen Mikael Lindstr?m Antti Rautio Erno Saukko 《Integral Equations and Operator Theory》2012,72(2):151-157
For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCj{uC_\varphi} on the weighted Banach spaces of analytic functions in terms of the analytic function
u \colon \mathbb D ? \mathbb C{u \colon \mathbb D \to \mathbb C} and the nth power of the analytic selfmap j{\varphi} of the open unit disc
\mathbb D{\mathbb D} . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general
radial weights. 相似文献
3.
Consider j = f +[`(g)]\varphi = f + \overline {g}, where f and g are polynomials, and let TjT_{\varphi} be the Toeplitz operators with the symbol j\varphi. It is known that if TjT_{\varphi} is hyponormal then |f¢(z)|2 3 |g¢(z)|2|f'(z)|^{2} \geq |g'(z)|^{2} on the unit circle in the complex plane. In this paper, we show that it is also a necessary and sufficient condition under
certain assumptions. Furthermore, we present some necessary conditions for the hyponormality of TjT_{\varphi} on the weighted Bergman space, which generalize the results of I. S. Hwang and J. Lee. 相似文献
4.
Yong Fang 《Geometriae Dedicata》2010,145(1):139-150
Let g be a negatively curved Riemannian metric of a closed C
∞ manifold M of dimension at least three. Let L
λ be a C
∞ one-parameter convex superlinear Lagrangian on TM such that
L0(v) = \frac12 g(v, v){L_0(v)= \frac{1}{2} g(v, v)} for any v ∈ TM. We denote by jl{\varphi^\lambda} the restriction of the Euler-Lagrange flow of L
λ on the
\frac12{\frac{1}{2}} -energy level. If λ is small enough then the flow jl{\varphi^\lambda} is Anosov. In this paper we study the geometric consequences of different assumptions about the regularity of the Anosov
distributions of jl{\varphi^\lambda} . For example, in the case that the initial Riemannian metric g is real hyperbolic, we prove that for λ small, jl{\varphi^\lambda} has C
3 weak stable and weak unstable distributions if and only if jl{\varphi^\lambda} is C
∞ orbit equivalent to the geodesic flow of g. 相似文献
5.
Constantin Costara 《Integral Equations and Operator Theory》2012,73(1):7-16
Let X be a complex Banach space and let B(X){\mathcal{B}(X)} be the space of all bounded linear operators on X. For x ? X{x \in X} and T ? B(X){T \in \mathcal{B}(X)}, let rT(x) = limsupn ? ¥ || Tnx|| 1/n{r_{T}(x) =\limsup_{n \rightarrow \infty} \| T^{n}x\| ^{1/n}} denote the local spectral radius of T at x. We prove that if j: B(X) ? B(X){\varphi : \mathcal{B}(X) \rightarrow \mathcal{B}(X)} is linear and surjective such that for every x ? X{x \in X} we have r
T
(x) = 0 if and only if rj(T)(x) = 0{r_{\varphi(T)}(x) = 0}, there exists then a nonzero complex number c such that j(T) = cT{\varphi(T) = cT} for all T ? B(X){T \in \mathcal{B}(X) }. We also prove that if Y is a complex Banach space and j:B(X) ? B(Y){\varphi :\mathcal{B}(X) \rightarrow \mathcal{B}(Y)} is linear and invertible for which there exists B ? B(Y, X){B \in \mathcal{B}(Y, X)} such that for y ? Y{y \in Y} we have r
T
(By) = 0 if and only if rj( T) (y)=0{ r_{\varphi ( T) }(y)=0}, then B is invertible and there exists a nonzero complex number c such that j(T) = cB-1TB{\varphi(T) =cB^{-1}TB} for all T ? B(X){T \in \mathcal{B}(X)}. 相似文献
6.
R. Ger 《Aequationes Mathematicae》2000,60(3):268-282
Summary. Quite recently C. Alsina, P. Cruells and M. S. Tomás [2], motivated by F. Suzuki's property of isosceles trapezoids, have proposed the following orthogonality relation in a real normed linear space (X, ||·||) (X, \Vert \cdot \Vert) : two vectors x,y ? X x,y \in X are T-orthogonal whenever¶||z-x ||2 + ||z-y ||2 = ||z ||2 + ||z-(x+y) ||2 \Vert z-x \Vert^2 + \Vert z-y \Vert^2 = \Vert z \Vert^2 + \Vert z-(x+y) \Vert^2 ¶for every z ? X z \in X . A natural question arises whether an analogue of T-orthogonality may be defined in any real linear space (without a norm structure). Our proposal reads as follows. Given a functional j \varphi on a real linear space X we say that two vectors x,y ? X x,y \in X are j \varphi -orthogonal (and write x^jy x\perp_{\varphi}y ) provided that Dx,yj = 0 \Delta_{x,y}\varphi = 0 (Dh1,h2 \Delta_{h_1,h_2} stands here and in the sequel for the superposition Dh1 °Dh2 \Delta_{h_1} \circ \Delta_{h_2} of the usual difference operators).¶We are looking for necessary and/or sufficient conditions upon the functional j \varphi to generate a j \varphi -orthogonality such that the pair X,^j X,\perp_{\varphi} forms an orthogonality space in the sense of J. Rätz (cf. [6]). Two new characterizations of inner product spaces as well as a generalization of some results obtained in [2] are presented. 相似文献
7.
On the iterates of Euler's function 总被引:1,自引:0,他引:1
R. Warlimont 《Archiv der Mathematik》2001,76(5):345-349
Asymptotic representations are given for the three sums ?n £ x j(n)/j(j(n))\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr ), ?n £ x j(n)/j(j(n))\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr ), ?n £ x log j(n)/j(j(n)) ; j\textstyle\sum\limits \limits _{n\le x}\ \log \, \varphi (n)/\varphi \bigl (\varphi (n)\bigr )\ ; \ \varphi is Euler's function. 相似文献
8.
Misha Verbitsky 《Mathematische Zeitschrift》2010,264(4):939-957
Let (M, ω) be a Kähler manifold. An integrable function ${\varphi}Let (M, ω) be a K?hler manifold. An integrable function j{\varphi} on M is called ω
q
-plurisubharmonic if the current ddcjùwq-1{dd^c\varphi\wedge \omega^{q-1}} is positive. We prove that j{\varphi} is ω
q
-plurisubharmonic if and only if j{\varphi} is subharmonic on all q-dimensional complex subvarieties. We prove that a ω
q
-plurisubharmonic function is q-convex, and admits a local approximation by smooth, ω
q
-plurisubharmonic functions. For any closed subvariety Z ì M{Z\subset M} ,
dim\mathbbC Z £ q-1{\dim_\mathbb{C} Z\leq q-1} , there exists a strictly ω
q
-plurisubharmonic function in a neighbourhood of Z (this result is known for q-convex functions). This theorem is used to give a new proof of Sibony’s lemma on integrability of positive closed (p, p)-forms which are integrable outside of a complex subvariety of codimension ≥ p + 1. 相似文献
9.
John R. Akeroyd Pratibha G. Ghatage Maria Tjani 《Integral Equations and Operator Theory》2010,68(4):503-517
For any analytic self-map j{\varphi} of {z : |z| < 1} we give four separate conditions, each of which is necessary and sufficient for the composition operator Cj{C_{\varphi}} to be closed-range on the Bloch space B{\mathcal{B}} . Among these conditions are some that appear in the literature, where we provide new proofs. We further show that if Cj{C_{\varphi}} is closed-range on the Bergman space
\mathbbA2{\mathbb{A}^2} , then it is closed-range on B{\mathcal{B}} , but that the converse of this fails with a vengeance. Our analysis involves an extension of the Julia-Carathéodory Theorem. 相似文献
10.
Examples of factorial threefolds complete intersection in $${\mathbb{P}^5}$$ with many singularities
Pietro Sabatino 《Ricerche di matematica》2009,58(2):285-297
Denote by ν
m
(d) the maximal integer for which there exists for d >> 0{d \gg 0} a threefold
X ì \mathbbP5{X\subset \mathbb{P}^5} complete intersection of hypersurfaces of degree respectively d and d − 1 such that X has only ordinary singularities of order m and |Sing(X)| = ν
m
(d). We prove that, nm(d) 3 j(d){\nu_m(d)\ge \varphi(d)} where j(d) ~ d5{\varphi(d)\sim d^5} asymptotically. This result extends (Di Gennaro and Franco in Commun Contemp Math 10(5):745–764, 2008, Corollary 2.10). 相似文献
11.
12.
Let X be a realcompact space and H:C(X)?\mathbbR{H:C(X)\rightarrow\mathbb{R}} be an identity and order preserving group homomorphism. It is shown that H is an evaluation at some point of X if and only if there is j ? C(\mathbbR){\varphi\in C(\mathbb{R})} with ${\varphi(r)>\varphi(0)}${\varphi(r)>\varphi(0)} for all r ? \mathbbR-{0}{r\in\mathbb{R}-\{0\}} for which H°j = j°H{H\circ\varphi=\varphi\circ H} . This extends (and unifies) classical results by Hewitt and Shirota. 相似文献
13.
In this paper, we construct a new family of harmonic morphisms ${\varphi:V^5\to\mathbb{S}^2}In this paper, we construct a new family of harmonic morphisms
j:V5?\mathbbS2{\varphi:V^5\to\mathbb{S}^2}, where V
5 is a 5-dimensional open manifold contained in an ellipsoidal hypersurface of
\mathbbC4 = \mathbbR8{\mathbb{C}^4\,=\,\mathbb{R}^8}. These harmonic morphisms admit a continuous extension to the completion V*5{{V^{\ast}}^5}, which turns out to be an explicit real algebraic variety. We work in the context of a generalization of the Hopf construction
and equivariant theory. 相似文献
14.
Carme Cascante Joan Fàbrega Daniel Pascuas 《Integral Equations and Operator Theory》2011,69(3):373-391
For weighted Toeplitz operators TNj{{\mathcal T}^N_\varphi} defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions f to the equation TNj(f)=h{{\mathcal T}^N_\varphi(f)=h} in terms of the regularity of the symbol φ and the data h. As an application, we deduce that if
f\not o 0{f\not\equiv0} is a function in the Hardy space H
1 such that its argument [`(f)]/f{\bar f/f} is in a Lipschitz space on the unit sphere
\mathbb S{{\mathbb S}}, then f is also in the same Lipschitz space, extending a result of Dyakonov to several complex variables. 相似文献
15.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
16.
Mohamed Tahar Kadaoui Abbassi Oldřich Kowalski 《Annals of Global Analysis and Geometry》2010,38(1):11-20
We prove that there is always a locally homogeneous Einstein g-natural metric on the unit tangent sphere bundle over any Riemannian space of constant positive sectional curvature. Furthermore,
using the (1–1) correspondence between all SO(m + 1)-invariant homogeneous metrics on the Stiefel manifold
V2 \mathbbRm+1 = SO(m+1)/SO(m-1){V_2 \mathbb{R}^{m+1} = {{SO}}(m+1)/{{SO}}(m-1)} and all g-natural metrics on T1 Sm{T_1 S^m} (Abbassi and Kowalski, Diff. Geom. Appl., to appear [7]), we reconstruct, by purely local procedure, the same well-known
unique SO(m + 1)-invariant homogeneous Einstein metric on
V2 \mathbbRm+1, m 1 3{V_2 \mathbb{R}^{m+1}, m \neq 3}, initially constructed by Kobayashi. 相似文献
17.
In this article we study the abstract two parameter eigenvalue problem $$\begin{gathered} T_1 u_1 = \left( {\lambda _1 V_{11} + \lambda _2 V_{12} } \right)u_1 , \left\| {u_1 } \right\| = 1 \hfill \\ T_2 u_2 = \left( {\lambda _1 V_{21} + \lambda _2 V_{22} } \right)u_2 , \left\| {u_2 } \right\| = 1 \hfill \\ \end{gathered}$$ where, in the Hilbert spaces Hj, Tj is self-adjoint, bounded below and has compact resolvent, and Vjk are self-adjoint bounded operators, (?1)j+kVjk >> 0, j, k = 1, 2. An eigenvalue λ for this problem is a point in R2 satisfying both equations. Under appropriate conditions, the eigenvalues λn = (λ1 n, λ2 n) are countable and in R2. We aim to describe the set of limit points of λn/∥λn∥, as ∥λn∥ → ∞, in terms of the Vjk. 相似文献
18.
Jan A. van Casteren 《Journal of Evolution Equations》2011,11(2):457-476
Let
(tj)j ? \mathbbN{\left(\tau_j\right)_{j\in\mathbb{N}}} be a sequence of strictly positive real numbers, and let A be the generator of a bounded analytic semigroup in a Banach space X. Put
An=?j=1n(I+\frac12 tjA) (I-\frac12 tjA)-1{A_n=\prod_{j=1}^n\left(I+\frac{1}{2} \tau_jA\right) \left(I-\frac{1}{2} \tau_jA\right)^{-1}}, and let x ? X{x\in X}. Define the sequence
(xn)n ? \mathbbN ì X{\left(x_n\right)_{n\in\mathbb{N}}\subset X} by the Crank–Nicolson scheme: x
n
= A
n
x. In this paper, it is proved that the Crank–Nicolson scheme is stable in the sense that
supn ? \mathbbN||Anx|| < ¥{\sup_{n\in\mathbb{N}}\left\Vert A_nx\right\Vert<\infty}. Some convergence results are also given. 相似文献
19.
Let
W ì \BbbR2\Omega \subset \Bbb{R}^2 denote a bounded domain whose boundary
?W\partial \Omega is Lipschitz and contains a segment G0\Gamma_0 representing
the austenite-twinned martensite interface. We prove
infu ? W(W) òW j(?u(x,y))dxdy=0\displaystyle{\inf_{{u\in \cal W}(\Omega)} \int_\Omega \varphi(\nabla
u(x,y))dxdy=0} 相似文献
20.
We construct an explicit intertwining operator L{\mathcal L} between the Schr?dinger group eit \frac\triangle2{e^{it \frac\triangle2}} and the geodesic flow on certain Hilbert spaces of symbols on the cotangent bundle T*X Γ of a compact hyperbolic surface X Γ = Γ\D. We also define Γ-invariant eigendistributions of the geodesic flow PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} (Patterson-Sullivan distributions) out of pairs of \triangle{\triangle} -eigenfunctions, generalizing the diagonal case j = k treated in Anantharaman and Zelditch (Ann. Henri Poincaré 8(2):361–426, 2007). The operator L{\mathcal L} maps PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} to the Wigner distribution WGj,k{W^{\Gamma}_{j,k}} studied in quantum chaos. We define Hilbert spaces HPS{\mathcal H_{PS}} (whose dual is spanned by {PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}}}), resp. HW{\mathcal H_W} (whose dual is spanned by {WGj,k}{\{W^{\Gamma}_{j,k}\}}), and show that L{\mathcal L} is a unitary isomorphism from HW ? HPS.{\mathcal H_{W} \to \mathcal H_{PS}.} 相似文献