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1.
We prove L
r
estimates for the Dirichlet problem –div(a(x,u,Du))=f with f in L
q
for 1q+, where the operator satisfies (|s|)||
p
a(x,s,), with p>1. These estimates are obtained without symmetrization and are sharp in some cases. 相似文献
2.
Horst Elmar Winkelnkemper 《Annals of Global Analysis and Geometry》1992,10(3):209-218
Let
t
be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M
n
, whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d
t
and, for each x M, we define a smooth real function
x
(t) : (1 +
i
(t)), where the i(t) are the eigenvalues of AA
T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t
, restricted to v at the point x
-t M
n.Among other things, we prove the
Theorem (Theorem II, below). Assume v is also volume preserving and that
x
'
(t) 0 for all x M and real t; then, if
x
t
: M M is weakly missng for some t, it is necessary that vx 0 at all x M. 相似文献
3.
Paul Günther 《Annals of Global Analysis and Geometry》1994,12(1):219-236
LetM
t[](x) be the spherical mean value operator applied to a function on a symmetric Riemannian space of the non-compact type.L
—decay estimations forM
t
[](x) as well as for its derivatives with respect to (t, x) are given, provided that belongs to a Banach space with suitable weighted supremum norm. This leads to estimates of the solutions to the wave equation in certain cases in which Huygens' principle is valid. 相似文献
4.
R. K. Getoor 《Potential Analysis》1995,4(1):79-100
SupposeX is a Borel right process andm is a -finite excessive measure forX. Given a positive measure not chargingm-semipolars we associate an exact multiplicative functionalM(). No finiteness assumptions are made on . Given two such measures and ,M()=M() if and only if and agree on all finely open measurable sets. The equation (q–L)u+u=f whereL is the generator of (a subprocess of)X may be solved for appropriatef by means of the Feynman-Kac formula based onM(). Both uniqueness and existence are considered.Supported in part by NSF Grant DMS 92-24990. 相似文献
5.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
6.
Approximation by Reciprocals of Polynomials with Positive Coefficients in L
p
Spaces 总被引:5,自引:0,他引:5
We prove that, if f(x) L
p
[0,1], 1 < p < , f(x) 0, x [0,1], f 0, then there is a polynomial p(x) +
n
such that f - 1/p
LP
C(p)(f,n
-1/2)
LP
where +
n
indicates the set of all polynomials of degree n with positive coeficients (see the definition (1) in the text). 相似文献
7.
We show that for each positive integer n there is a finite list of equivalence relations on []
n
with the property that for every other equivalence relation E on []
n
there is X of order type equal to the order type of , such that E[X]
n
is equal to one of the equivalence relations from the list. 相似文献
8.
9.
Questions of approximative nature are considered for a space of functions L
p(G, ), 1 p , defined on a locally compact abelian Hausdorff group G with Haar measure . The approximating subspaces which are analogs of the space of exponential type entire functions are introduced. 相似文献
10.
Paul Jolissaint 《K-Theory》1989,2(6):723-735
We associate to any length function L on a group a space of rapidly decreasing functions on (in the l
2 sense), denoted by H
L
(). When H
L
() is contained in the reduced C*-algebra C
r
*
() of (), then it is a dense *-subalgebra of C
r
*
() and we prove a theorem of A. Connes which asserts that under this hypothesis H
L
() has the same K-theory as C
r
*
(). We introduce another space of rapidly decreasing functions on (in the l
1 sense), denoted by H
L
1,
(), which is always a dense *-subalgebra of the Banach algebra l
1(), and we show that H
L
1,
() has the same K-theory as l
1(). 相似文献
11.
Elmar Schrohe 《Annals of Global Analysis and Geometry》1992,10(3):237-254
The pseudodifferential operators with symbols in the Grushin classes \~S
inf0
sup,
, 0 < 1, of slowly varying symbols are shown to form spectrally invariant unital Frécher-*-algebras (*-algebras) in L(L
2(R
n
)) and in L(H
st
) for weighted Sobolev spaces H
inf
supst
defined via a weight d function . In all cases, the Fredholm property of an operator can be characterized by uniform ellipticity of the symbol. This gives a converse to theorems of Grushin and Kumano-Ta-Taniguchi. Both, the spectrum and the Fredholm spectrum of an operator turn out to be independent of the choices of s, t and .The characterization of the Fredholm property by uniform ellipticity leads to an index theorem for the Fredholm operators in these classes, extending results of Fedosov and Hörmander. 相似文献
12.
J.C. Mason 《Numerical Algorithms》2005,38(1):61-78
By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [–1,1], as well as (L
) minimax properties, and best L
1 sufficiency requirements based on Chebyshev interpolation. Finally we establish best L
p
, L
and L
1 approximation by partial sums of lacunary Chebyshev series of the form
i=0
a
i
b
i(x) where
n
(x) is a Chebyshev polynomial and b is an odd integer 3. A complete set of proofs is provided. 相似文献
13.
Shiquan WU 《应用数学学报(英文版)》1996,12(4):377-383
Letn, s
1,s
2, ... ands
n
be positive integers. Assume
is an integer for eachi}. For
,
, and
, denotes
p
(a)={j|1jn,a
j
p},
, and
.
is called anI
t
p
-intersecting family if, for any a,b
,a
i
b
i
=min(a
i
,b
i
)p for at leastt i's.
is called a greedyI
t
P
-intersecting family if
is anI
t
p
-intersecting family andW
p
(A)W
p
(B+A
c
) for anyAS
p
(
) and any
with |B|=t–1.In this paper, we obtain a sharp upper bound of |
| for greedyI
t
p
-intersecting families in
for the case 2ps
i
(1in) ands
1>s
2>...>s
n
.This project is partially supported by the National Natural Science Foundation of China (No.19401008) and by Postdoctoral Science Foundation of China. 相似文献
14.
If S is an H-cone and P:SS is a localizable dilation operator on S (i.e., P is additive increasing, contractive, continuous in order from below and s(Ps+t–Pt+Pf)S, s,tS,f(S–S)+), then it is proved that its adjoint P
*:S
*S
* (i.e., P
*=P) is also a localizable dilation operator. This is an improvement of a result obtained by G. Mokobodzki in the frame of excessive functions. 相似文献
15.
We construct a Rankin Selberg integral to represent the exterior cube L function L(,3,s) of an automorphic cuspidal module of GL6(
F
) (where F is a number field). We determine the poles of this L function and find period conditions for the special value L(,3,1/2). We use the Siegal Weil formula. We also state an analogue of the Gross–Prasad conjecture concerning a criterion for the nonvanishing of L(,3,1/2). 相似文献
16.
We use the eta invariant to study the connective K-theory groups ko
m
(B
) of the classifying space for the cyclic group where - 2 2. 相似文献
17.
Let
n
be n-dimensional Euclidean space, and let : [0, L]
n
and : [0, L]
n
be closed rectifiable arcs in
n
of the same total length L which are parametrized via their arc length. is said to be a chord-stretched version of if for each 0s tL, |(t)–(s)| |(t)–(s)|. is said to be convex if is simple and if ([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if were simple then there existed a convex chord-stretched version of . This result led Professor Yang Lu to conjecture that if were convex and were a chord-stretched version of then and would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where and are C
2 curves. In this paper we prove the conjecture in general. 相似文献
18.
Pablo Pedregal 《Applied Mathematics and Optimization》1993,28(1):1-10
This paper shows the property of weak lower semicontinuity of separately convex integrands under more general hypothesis than boundedness inL
2 of partial derivatives, and some properties of the parametrized measures associated with such sequences.This research was partially supported by DGICYT (Spain) through Programa de Perfeccionamiento y Movilidad de Personal Investigador and through Grant PB 90-245. 相似文献
19.
Robert Schmidt Donald A. DaDeppo 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(6):991-1004
Zusammenfassung Auf Grund der Hypothesen von Ebenbleiben und Normalität der Querschnitte werden die Differentialgleichungen der nichtlinearen Theorie der Bogenträger abgeleitet und im Falle des schlanken, durch Einzellasten belasteten Kreisbogenträgers mit undehnbarer Mittellinie auf die Form der Pendelgleichung gebracht. Diese Gleichung wird dann benutzt, um die grossen Durchbiegungen und die Spannungsresultierenden eines Zweigelenkkreisbogens, der durch eine lotrechte exzentrische Einzellast belastet wird, zu berechnen. In der Nähe der kritischen Last bewirken kleine Exzentrizitäten bedeutende Grössenänderungen der Spannungsresultierenden und der Durchbiegungen.
Notation A cross-sectional area of curved beam - a radius of centroidal circle - E modulus of elasticity - e eccentricity of the load (Fig. 2) - F an arbitrary function - H horizontal component of the internal forceR acting on a cross section of the arch rib (Fig. 2) - h P horizontal displacement of the loadP (Fig. 2) - I moment of inertia of the cross-sectional area - k 2 =4p 2/(1+4p 2 sin20) - L span (distance between supports),L=2a sin - M internal bending couple (Figs. 1 and 2) - N internal normal tensile force (Figs. 1 and 2) - n distributed tangential load (Fig. 1) - P downward point load (Fig. 2) - p 2 –R a 2 /E I - Q internal shearing force (Figs. 1 and 2) - q distributed normal load (Fig. 1) - R internal resultant force (Fig. 2);R 2=H 2+V 2=N 2+Q 2 - radius of curvature of the undeformed centroidal curve - s length along the unextended centroidal curve measured from the left support - length along the unextended centroidal curve measured from the right support - u tangential displacement component of the centroidal curve (Fig. 1) - V vertical component ofR (Fig. 2) - v P vertical displacement of the loadP (Fig. 2) - w normal displacement component (Fig. 1) - x, y rectangular coordinates of the deformed left portion of the centroidal curve (Fig. 2) - Z - z normal distance (positive inward) from centroidal curve (Fig. 1) - half subtending angle of the arch (Fig. 2) - angle of rotation of the centroidal curve (Fig. 1) - extensional strain of the centroidal curve - z extensional strain of the linez=constant - y cos–x sin - angle between the tangent to the formed left portion of the centroidal curve and the horizontal (Fig. 2) - (u–w)/r, whereu=du/dø - angle betweenH andR - x cos+y sin - normal stress along the centroidal curve - z normal stress along the linez=constant - angle measured from the radius at the left support of the undeformed arch - (–)/2 (Fig. 2) - (+u)/r, where =d/dø A bar over a letter indicates that the entity pertains to the right portion of the arch. Asterisk indicates the deformed configuration. Primes indicate derivatives with respect to ø. 相似文献
Notation A cross-sectional area of curved beam - a radius of centroidal circle - E modulus of elasticity - e eccentricity of the load (Fig. 2) - F an arbitrary function - H horizontal component of the internal forceR acting on a cross section of the arch rib (Fig. 2) - h P horizontal displacement of the loadP (Fig. 2) - I moment of inertia of the cross-sectional area - k 2 =4p 2/(1+4p 2 sin20) - L span (distance between supports),L=2a sin - M internal bending couple (Figs. 1 and 2) - N internal normal tensile force (Figs. 1 and 2) - n distributed tangential load (Fig. 1) - P downward point load (Fig. 2) - p 2 –R a 2 /E I - Q internal shearing force (Figs. 1 and 2) - q distributed normal load (Fig. 1) - R internal resultant force (Fig. 2);R 2=H 2+V 2=N 2+Q 2 - radius of curvature of the undeformed centroidal curve - s length along the unextended centroidal curve measured from the left support - length along the unextended centroidal curve measured from the right support - u tangential displacement component of the centroidal curve (Fig. 1) - V vertical component ofR (Fig. 2) - v P vertical displacement of the loadP (Fig. 2) - w normal displacement component (Fig. 1) - x, y rectangular coordinates of the deformed left portion of the centroidal curve (Fig. 2) - Z - z normal distance (positive inward) from centroidal curve (Fig. 1) - half subtending angle of the arch (Fig. 2) - angle of rotation of the centroidal curve (Fig. 1) - extensional strain of the centroidal curve - z extensional strain of the linez=constant - y cos–x sin - angle between the tangent to the formed left portion of the centroidal curve and the horizontal (Fig. 2) - (u–w)/r, whereu=du/dø - angle betweenH andR - x cos+y sin - normal stress along the centroidal curve - z normal stress along the linez=constant - angle measured from the radius at the left support of the undeformed arch - (–)/2 (Fig. 2) - (+u)/r, where =d/dø A bar over a letter indicates that the entity pertains to the right portion of the arch. Asterisk indicates the deformed configuration. Primes indicate derivatives with respect to ø. 相似文献
20.
Given a nuclear b-space N, we show that if is a finite or -finite measure space and 1p, then the functors L
loc
p
(,N.) and NL
p
(,.) are isomorphic on the category of b-spaces of L. Waelbroeck. 相似文献