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1.
Let K be a field of characteristic 2 and letV be a vector space of dimension 2m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2m, K) acts on the exterior powers k V for 0 k. 2m There is a contraction map defined on the exterior algebra , which commutes with the Sp(2m, K) action and satisfies 2 = 0 and ( k V) k–1 V We prove that ( k V)= ker k–1 V except when k=m+2. In the exceptional case, ( m+2 V) has codimension 2m in ker m V and we show that the quotient module ker m V/ m+2 V is a spin module for Sp(2m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in m V and multiplicity 0 in all other components of V.  相似文献   

2.
The behavior of the poles zn(), n=1,2,... of the scattering matrix of the operatorl u=–u(x), x , (u/n)+(x)u|=0 as 0 is considered. It is proved that |zn()–zn|=0((1/2)qn), where qn is the order of the pole of the scattering matrix for the operator 0u=–u, u/=0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 183–191, 1981.  相似文献   

3.
The problem of existence of wave operators for the Klein-Gordon equation ( t 2 –+2+iV1t+V2)u(x,t)=0 (x R n,t R, n3, >0) is studied where V1 and V2 are symmetric operators in L2(R n) and it is shown that conditions similar to those of Veseli-Weidmann (Journal Functional Analysis 17, 61–77 (1974)) for a different class of operators are also sufficient for the Klein-Gordon equation.  相似文献   

4.
This paper concerns the investigation of the stabilization of solutions of the Cauchy problem for a system of equations of the form u/t = u + fi(u, v); v/t = v + F2(u, v). It is proved that under certain assumptions the behavior of solutions as t is determined by mutual arrangement of the set of initial conditions {(u, v): u = f1(x), v =f 2(x), xRn} and the trajectories of the system of ordinary differential equations du/dt = F1(u, v), dv/dt = F2(u, v). The question of stabilization of the solutions of a single quasilinear parabolic equation is also considered.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 85–92, January, 1968.  相似文献   

5.
We consider the nonlinear diffusion-absorption problem in L1() u - div a(, Du) + j (, u) f on , u = 0 on where is an arbitrary open set in N. Conditions for the existence of a strong solution are presented and the existence of a natural generalized solution in the general case is established. We study the dependence of the generalized solution on the absorption term j and characterize generalized solutions which are essentially bounded.  相似文献   

6.
In this paper it is proved that for any functionf L 2 [–; ], f>0, there exists a complete orthonormalized system of uniformly bounded trigonometric polynomials with respect to which the Fourier series of this function is divergent almost everywhere in the interval [–; ].Translated from Matematicheskie Zametki, Vol. 20, No. 1, pp. 69–78, July, 1976.The authoress expresses her gratitude to A. M.  相似文献   

7.
Summary In this paper we obtain an existence theorem for the abstract Cauchy problem for multivalued differential equations of the form u– f(u)+G(u), u(O)=x0, where f is the Fréchet subdifferential of a functionf defined on an open subset of a real separable Hilbert space H, taking its values in R {+} and G is a multifunction from C([0, T], ) into the nonempty subsets of L2([0, T], H). As an application we obtain an existence theorem for the multivalued perturbed problem x– f(x)+F(t, x), x(0)=x0, where F:[0, T]×(H) is a multifunction satisfying some regularity assumptions.  相似文献   

8.
Let a, a0, a, be a fixed point in the z-plane, (a, 0, ), the class of all systemsf k()l 3 of functions z=f k(), k=1, 2, 3, of which the first two map conformally and in a s ingle-sheeted manner the circle ¦¦<1, and the third maps in a similar manner the region ¦¦>1, into pair-wise nonintersecting regions Bk, k=1, 2, 3, containing the points a, 0, and , respectively, so thatf 1(0)=a,f 2(0)=0 andf 3()=. The region of values (a, 0, ) of the system M(¦f 1'(0)¦, ¦f 2'(0)¦, 1/¦f 3'()¦) in the class (a, 0, ) is determined.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 417–424, October, 1969.  相似文献   

9.
Let M be a Kähler manifold with Ricci and antiholomorphic Ricci curvature bounded from below. Let be a domain in M with some bounds on the mean and JN-mean curvatures of its boundary . The main result of this paper is a comparison theorem between the Mean Exit Time function defined on and the Mean Exit Time from a geodesic ball of the complex projective space n () which involves a characterization of the geodesic balls among the domain . In order to achieve this, we prove a comparison theorem for the mean curvatures of hypersurfaces parallel to the boundary of , using the Index Lemma for Submanifolds.Work partially supported by a DGICYT Grant No. PS87-0115-C03-01.  相似文献   

10.
We consider the question of integration of a multivalued operator T, that is the question of finding a function f such that Tf. If is the Fenchel–Moreau subdifferential, the above problem has been completely solved by Rockafellar, who introduced cyclic monotonicity as a necessary and sufficient condition. In this article we consider the case where f is quasiconvex and is the lower subdifferential <. This leads to the introduction of a property that is reminiscent to cyclic monotonicity. We also consider the question of the density of the domains of subdifferential operators.  相似文献   

11.
A partial regularity theorem is established for a particular class of weak solutions to the systemu/t– div(K(u)u)=(u)¦¦2, div((u))=0 on a bounded domain inR N . Under our assumptions, (u) may exhibit exponential decay, and thus the system may be degenerate. Our proof is based upon a blow-up argument.This work was supported in part by NSF Grant DMS9424448.  相似文献   

12.
Let (–1,1), let 2/(1–)p<, letp denote the Hölder conjugate ofp, and let be an open arc of the unit circle. It is shown that, iff is a holomorphic function on the unit disc such that: (i) (1–|z|)log+|f(z)| isL p -integrable on the sector {r:0f has an infinite asymptotic value has -finite (2–(1+)p)-dimensional Hausdorff, measure, thenf has finite angular limits on a subset of of positive linear measure. In fact, a stronger conclusion will be established.  相似文献   

13.
Hieber  Matthias  Schrohe  Elmar 《Positivity》1999,3(3):259-272
Let {T p:q 1 p q 2} be a family of consistent C 0 semigroups on L p(), with q 1,q 2 [1,) and open. We show that certain commutator conditions on T p and on the resolvent of its generator A p ensure the p independence of the spectrum of A p for p [q 1,q 2.Applications include the case of Petrovskij correct systems with Hölder continuous coefficients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coefficients.  相似文献   

14.
A Strong Maximum Principle for some quasilinear elliptic equations   总被引:37,自引:0,他引:37  
In its simplest form the Strong Maximum Principle says that a nonnegative superharmonic continuous function in a domain n ,n 1, is in fact positive everywhere. Here we prove that the same conclusion is true for the weak solutions of – u + (u) = f with a nondecreasing function ,(0)=0, andf0 a.e. in if and only if the integral((s)s) –1/2 ds diverges ats=0+. We extend the result to more general equations, in particular to – p u + (u) =f where p (u) = div(|Du| p-2 Du), 1 <p < . Our main result characterizes the nonexistence of a dead core in some reaction-diffusion systems.This work was partly done while the author was visiting the University of Minnesota as a Fulbright Scholar.  相似文献   

15.
Summary In this paper we solve the functional equationx(u + v)(u – v) = f 1(u)g1(v) + f2(u)g2(v) under the assumption thatx, , f 1, f2, g1, g2 are complex-valued functions onR n ,n N arbitrary, and 0 and 0 are continuous. Our main result shows that, apart from degeneracy and some obvious modifications, theta functions of one complex variable are the only continuous solutions of this functional equation.  相似文献   

16.
LetE be a vector lattice of real-valued functions defined on a setX, and (E):={{f1}:fE}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsfE is (E)--smooth iffX is (E)-complete. An application of this general result to various topological situations yields some new measure-theoretic characterizations of realcompact, Borel-complete andN-compact spaces, respectively.  相似文献   

17.
Summary It is shown that if (X, ) is a product of totally ordered measure spaces andf j (j=1,2,3,4) are measurable non-negative functions onX satisfyingf 1(x)f2(y)f3(xy)f4(xy), where (, ) are the lattice operations onX, then (f 1 d)(f 2 d)(f 3 d)(f 4 d). This generalises results of Ahlswede and Daykin (for counting measure on finite sets) and Preston (for special choices off j).  相似文献   

18.
Let X 1, , X n (n > p) be a random sample from multivariate normal distribution N p (, ), where R p and is a positive definite matrix, both and being unknown. We consider the problem of estimating the precision matrix –1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of –1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators.  相似文献   

19.
Summary We consider a (possibly) vector-valued function u: RN, Rn, minimizing the integral , 2-2/(n*1)<p<2, whereD i u=u/x i or some more general functional retaining the same behaviour, we prove higher integrability for Du: D1 u,..., Dn–1 u Lp/(p-1) and Dnu L2; this result allows us to get existence of second weak derivatives: D(D1 u),...,D(Dn–1u)L2 and D(Dn u) L p.This work has been supported by MURST and GNAFA-CNR.  相似文献   

20.
A -symplectic structure on a complex manifold M of complex dimension2n is given by a smooth -closed (2, 0)-form such that n is nonvanishing. We prove that a version of the Darboux theorem isvalid for such a structure: locally can be represented as i=1 n f i f n + i for appropriate smooth complex valuedfunctions f 1, ..., f 2n . We also present a contact version of this theorem.  相似文献   

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