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61.
Ruey-Jen Jang-Lewis Harold Dean Victory Jr. 《Integral Equations and Operator Theory》1994,18(1):88-108
LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL
p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T
x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter. 相似文献
62.
Oscillatory properties of a weak convergent sequence of functions bounded inL
p
, 1 ≤p ≤ ∞, may be summarized by the parametrized measure it generates. When such a measure is generated by the gradients of a sequence
of functions bounded inH
1,p
, it must have special properties. The purpose of this paper is to characterize such parametrized measures as the ones that
obey Jensen’s inequality for all quasiconvex functions with the appropriate growth at infinity. We have found subtle differences
between the casesp < ∞ andp = ∞. A consequence is that any measure determined by biting convergence is in fact generated by a sequence convergent in
a stronger sense. We also give a few applications.
Research groupTransitions and Defects in Ordered Materials, funded by the NSF, the AFOSR, and the ARO. The work of the second author is also supported by DGICYT (Spain) through “Programa
de Perfeccionamiento y Movilidad del Personal Investigador” and through Grant PB90-0245. 相似文献
63.
Erik G. F. Thomas 《Acta Appl Math》1996,43(2):191-232
We construct an analogue of the Feynman path integral for the case of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% aaaeaacaaIXaaabaGaamyAaaaadaWcaaqaaiabgkGi2cqaaiabgkGi% 2kaadshaaaqeduuDJXwAKbYu51MyVXgaiuaacqWFvpGAcaWG0bGaey% ypa0JaamisamaaBaaaleaacaGGOaaabeaakmaaBaaaleaacaGGPaaa% beaakiab-v9aQjaadshaaaa!4A8D!\[ - \frac{1}{i}\frac{\partial }{{\partial t}}\varphi t = H_( _) \varphi t\] in which H
() is a self-adjoint operator in the space L
2(M)= % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSOaHmkaaa!3744!\[\mathbb{C}\], where
M
is a finite set, the paths being functions of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSyhHekaaa!375D!\[\mathbb{R}\] with values in M. The path integral is a family of measures F
t,t with values in the operators on L
2(M), or equivalently, a family of complex measures corresponding to matrix coefficients.It is shown that these measures on path space are in some sense dominated by the measure of a Markov process. This implies that F
t,t is concentrated on the set of step functions S[t,t].This allows one to make sense of, and prove, the analogue of Feynman's formula for the propagator of the Hamiltonian H=H
0+V, where V is a potential, namely the formula: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyzamaaCa% aaleqabaGaeyOeI0IaamyAaiaacIcacaWG0bGaai4jaiabgkHiTiaa% dshacaGGPaGaamisaaaakiabg2da9maapebabaGaaeyzamaaCaaale% qabaGaeyOeI0IaamyAamaapedabaGaamOvaiaacIcatCvAUfKttLea% ryqr1ngBPrgaiuGacqWF4baEcaGGOaGaam4CaiaacMcacaGGPaGaae% izaiaabohaaWqaaiaadshaaeaacaWG0bGaai4jaaGdcqGHRiI8aaaa% kiaadAeadaWgaaWcbaGaamiDaiaacEcacaGGSaGaamiDaaqabaGcca% GGOaGaaeizaiab-Hha4jaacMcaaSqaaiaadofacaGGBbGaamiDaiaa% cYcacaWG0bGaai4jaiaac2faaeqaniabgUIiYdaaaa!6410!\[{\text{e}}^{ - i(t' - t)H} = \int_{S[t,t']} {{\text{e}}^{ - i\int_t^{t'} {V(x(s)){\text{ds}}} } F_{t',t} ({\text{d}}x)} \]and the corresponding formulas for the matrix coefficients, in which the integral extends over the paths beginning and ending in the appropriate points. We show that the measures F
t,t are completely determined by these equations and by a certain multiplicative property.The path integral corresponding to a two-particle system without interaction is the direct product of the corresponding path integrals. The propagator for a two-particle system with interaction can be obtained by repeated integration.Finally, we show that the above integral formula can be generalized to the case where the potential is time dependent. 相似文献
64.
Zhen-Qing Chen 《Potential Analysis》1996,5(4):383-401
Let D be an open set in d and E be a relatively closed subset of D having zero Lebesgue measure. A necessary and sufficient integral condition is given for the Sobolev spaces W
1,2 (D) and W
1,2(D\E) to be the same. The latter is equivalent to (normally) reflecting Brownian motion (RBM) on
being indistinguishable (in distribution) from RBM on
. This integral condition is satisfied, for example, when E has zero (d–1)-dimensional Hausdorff measure. Therefore it is possible to delete from D a relatively closed subset E having positive capacity but nevertheless the RBM on
is indistinguishable from the RBM on
, or equivalently, W
1,2(D\E)=W1,2(D). An example of such kind is: D=2 and E is the Cantor set. In the proof of above mentioned results, a detailed study of RBMs on general open sets is given. In particular, a semimartingale decomposition and approximation result previously proved in [3] for RBMs on bounded open sets is extended to the case of unbounded open sets.Research supported in part by NSF Grant DMS 86-57483. 相似文献
65.
We study Sobolev embedding theorems in Lorentz-Zygmund spaces. Some limiting cases are considered.Supported by M.U.R.S.T. (1990). 相似文献
66.
LetA be a von Neumann algebra and a faithful normal state. ThenO
= {
ºAd(g
1) :g G
A
}andU
= {
ºAd(u
*) :u U
A
are homogeneous reductive spaces. IfA is aC
* algebra,e
the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe
by invertible elements ofA can be imbedded inAA in such a way thate
is carried to 1 1 and the orbit ofe
to a homogeneous reductive space and an analytic submanifold ofAA. 相似文献
67.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If 46/xxlarge981.gif" alt="phiv" align="MIDDLE" BORDER="0"> is a surjective isometry of the separable symmetric operator spaceE(M, 46/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0">) associated with the approximately finite-dimensional semifinite factorM and if 46/xxlarge8741.gif" alt="par" align="MIDDLE" BORDER="0">·46/xxlarge8741.gif" alt="par" align="MIDDLE" BORDER="0">
E(M,46/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0">)
is not proportional to 46/xxlarge8741.gif" alt="par" align="MIDDLE" BORDER="0">·46/xxlarge8741.gif" alt="par" align="MIDDLE" BORDER="0">
L
2, then there exist a unitary operatorU46/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">M and a Jordan automorphismJ ofM such that46/xxlarge981.gif" alt="phiv" align="MIDDLE" BORDER="0">(x)=UJ(x) for allx46/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">M46/xxlarge8745.gif" alt="cap" align="MIDDLE" BORDER="0">E(M, 46/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0">). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, 46/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0">)).Research supported by the Australian Research Council 相似文献
68.
We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and 2-graded Lie algebras g = g0 + g1, where g0 = s0(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V =
p, q
of signature (p, q) and g1 is a spin 1/2 s0(V)-module extended to a s0-module with kernel V.As a result of the classification, we obtain, if g1 = S is the spinor module, the numbers L
+(n, s) (resp. L
–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L
+(–n, s)=L
–
(n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University). 相似文献
69.
70.
A. Ülger 《Monatshefte für Mathematik》1996,121(4):353-379
LetA be a commutative Banach algebra with a nonempty spectrum A. By weak we denote the relative weak topology induced on A by (A
*,A
**). In this note we study some properties of the topological space (A, weak) and present some applications of the results obtained and tools used to amenability, weakly compact homomorphisms, weakly compact subsets of the spectrum of the uniform algebras and to a characterization of the synthesizable ideals of the algebraA. 相似文献