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1.
Résumé Soit (V )0 une résolvante définie sur un espace mesurable telle que le noyau initial est borné; on trouve une condition nécéssaire et suffisante pour qu'un noyau borné U possède une résolvante (U )0 telle que U V pour tout 0. On donne plusieurs applications de ce résultat.  相似文献   

2.
We prove that if aC 1 smooth change of variable : generates a bounded composition operatorff° in the spaceA p()=L p ,p2, then is linear (affine).We also prove that for a nonlinearC 1 mapping , the norms of exponentialse i as Fourier multipliers inL p () tend to infinity (,||). In both results the condition C 1 is sharp, it cannot be replaced by the Lipschitz condition.  相似文献   

3.
It is shown that two real functionsf andg, defined on a real intervalI, satisfy the inequalitiesf(x + (1 – )y) g(x) + (1 – )g(y) andg(x + (1 – )y) f(x) + (1 – )f(y) for allx, y I and [0, 1], iff there exists an affine functionh: I such thatf h g. As a consequence we obtain a stability result of Hyers—Ulam type for affine functions.  相似文献   

4.
We consider an equation of infinite order in generalized derivatives in the sense of A. O. Gel'fond with a characteristic function of finite order L()=L1()... Ln(). It is explained by a purely analytical method (by the application of an interpolational method) when any solution of the equation is the sum of the solutions of similar equations with the characteristic functions L1(), ..., Ln(). In the case of an equation in ordinary derivatives, when L() is a function of exponential type, the problem is solved by the application of algebraic and functional methods of V. V. Napalkov [1].Translated from Matematicheskie Zametki, Vol. 18, No. 5, pp. 735–752, November, 1975.  相似文献   

5.
Let m , 0 m+ in Kato's class. We investigate the spectral function s( + m) where s( + m) denotes the upper bound of the spectrum of the Schrödinger operator + m. In particular, we determine its derivative at 0. If m- is sufficiently large, we show that there exists a unique 1 > 0 such that s( + 1m) = 0. Under suitable conditions on m+ it follows that 0 is an eigenvalue of + 1m with positive eigenfunction.  相似文献   

6.
We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if > then the logic with the quantifier there exist many is (,)-compact if and only if either is weakly compact or is singular of cofinality<. As a corollary, for every infinite cardinals and , there exists a (,)-compact non-(,)-compact logic if and only if either < orcf<cf or < is weakly compact.Counterexamples are given showing that the above statements may fail, ifV=L is not assumed.However, without special assumptions, analogous results are obtained for the stronger notion of [,]-compactness.  相似文献   

7.
We establish some reverse inequalities. We give applications to nonlinear elliptic boundary value problems containing a parameter which have two branches of solutions u (0) and U (>0) of which the first is continuous at the origin and the second increases indefinitely as 0.  相似文献   

8.
LetE be a Dedekind complete complex Banach lattice and letD denote the diagonal projection from the spaceL r (E) onto the centerZ(E) ofE. Let {T(t)} t0 be a positive strongly continuous semigroup of linear operators with generatorA. The first main result is that if the spectral bounds(A) equals to zero, then the functionD(T(t)) is a center valuedp-function. The second main result is that if for >0 the diagonalD(R(, A)) of the resolvent operatorR(, A) is strictly positive, then (D(R(, A))) –1 is a center valued Bernstein function. As an application of these results it follows that the order limit lim0D(R(,A)) exists inZ(E) and equals the order limit lim m D((R(, A)) m ) for any >0.  相似文献   

9.
Among other results, it is shown that ifC andK are arbitrary complexn×n matrices and if det( 0 2 I0 C+K)=0 for some 00 (resp. 0=0), then the Newton diagram of the polynomialt(, ) = det(2 I+(1+)C+K expanded in (–0) and , has at least a point on or below the linex+y=b (resp. has no expanded in (–0) and , has at least a point on or below the of 0 as an eigenvalue of 0 2 I+0 C+K. These are extensions of similar results deu to H. Langer, B. Najman, and K. Veseli proved for diagonable matricesC, and shed light on the eigenvalues of the perturbed quadratic matrix polynomials. Our proofs are independent and seem to be simpler  相似文献   

10.
Given a bounded linear operatorA in an infinite dimensional Banach space and a compact subset of a connected component of its semi-Fredholm domain, we construct a finite rank operatorF such that –A+F is bounded below (or surjective) for each ,F 2=0 and rankF=max min{dimN(–A), codimR(–A)}, if ind(–A)0 (or ind(–A)0, respectively) for each .  相似文献   

11.
An (m, n, k, 1,2) divisible difference set in a groupG of ordermn relative to a subgroupN of ordern is ak-subsetD ofG such that the list {xy–1:x, y D} contains exactly 1 copies of each nonidentity element ofN and exactly 2 copies of each element ofG N. It is called semi-regular ifk > 1 and k2=mn2. We develop a method for constructing a divisible difference set as a product of a difference set and a relative difference set or a difference set and a subset ofG which we call a relative divisible difference set. The method results in several parametrically new families of semi-regular divisible difference sets.  相似文献   

12.
This paper proves the existence of resolvable block designs with divisibility into groups GD(v; k, m; 1, 2) without repeated blocks and with arbitrary parameters such that 1 = k, (v–1)/(k–1) 2 vk–2 (and also 1 k/2, (v–1)/(2(k–1)) 2 vk–2 in case k is even) k 4 andp=1 (mod k–1), k < p for each prime divisor p of number v. As a corollary, the existence of a resolvable BIB-design (v, k, ) without repeated blocks is deduced with X = k (and also with = k/2 in case of even k) k , where a is a natural number if k is a prime power and=1 if k is a composite number.Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 623–634, April, 1976.  相似文献   

13.
Under minimal requirements on the coefficients and the boundary of the domain it is proved that the spectrum of the first boundary-value problem for an elliptic operator of second order always lies in the half-plane Re , where is the leading eigenvalue to which there corresponds a nonnegative eigenfunction. On the line Re = , there are no other points of the spectrum.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 351–358, September, 1976.  相似文献   

14.
We consider a multivalued BVP x'(t) A(t)x((t))+ F(t,x((t))), Lx= . Under appropriate assumptions on A, L and F, we prove that for sufficiently small the set of solutions to this problem is a nonempty infinite dimensional AR-space (Theorem 4).  相似文献   

15.
Thewidth (chain number) of a partial order P, < is the smallest cardinal such that ¦A¦< 1 + whenever A is an antichain (chain) in P. We prove that, if a partial order (P, <) has width and cf()=, then P contains antichains An (n<) such that ¦A 0¦<¦A1¦ <...<={¦An¦: n < < } and either A01 A2< ... or A0>A1 >A2> ... A similar structure result is obtained for partial orders with chain number if cf()=. As an application we solve a problem of van Douwen, Monk and Rubin [1] by showing that if a Boolean algebra has width , thencf() .This work has been partially supported by NATO grant No. 339/84.Presented by Bjarni Jonsson.  相似文献   

16.
We study a certain type of functional equation, which is of significance from the view point of systems of difference equations. Let the characteristic values of the system be and The case that either || > 1 or 0 < || < 1 has been treated in a former paper. The case that = 1, || = 1 with 1 will be given in another paper. The present note deals with the case = = 1, the most difficult case.AMS Subject Classification (1991): 39A10 39B05  相似文献   

17.
Summary Real hypersurfaces of an almost Hermitian manifold naturally admit an almost contact metric structure and the (f, g, u, v, w, , , )-structure is defined on submanifolds of codimension 3 of an almost Hermitian manifold. We study the so-called semi-invariant submanifolds of a complex space form with almost contact metric compound structure which is a general notion of (f, g, u, v, w, , , )-structure.Dedicated to professor Eulyong Pak on his 60th birthdayThis research was partially supported by Korean Science and Engineering Foundation Grant.  相似文献   

18.
Summary We consider the equation u+ expu=0, >0,u(boundary)0 in the formv= exp (K,v), whereK –1=–. We give bounds on for the latter equation to be solvable by the contraction mapping principle, and estimate theL 2 norm of the solution so obtained. We also give a bound on for the topological index of the solution to be non-zero and apply Krasnoselskii's results to the least squares method of approximating the solution.
Sommario Consideriamo l'equazione u+ expu=0, >0,u(frontiera)=0 nella formav= exp (Kv), doveK –1=–. In questo lavoro diamo limitazioni per per cui la seconda equazione e risolubile col metodo delle contrazioni, e diamo una stima della norma inL 2 della soluzione cosi ottenuta. Diamo anche una limitazione per per cui l'indice topologico della soluzione diventa non zero, e applichiamo i risultati di Krasnoselskii al metodo dei minimi quadrati per approssimare la soluzione.
  相似文献   

19.
Let T- S, be a family of not necessarily bounded semi-Fredholm operators, where T and S are operators acting between Banach spaces X and Y, and where S is bounded with D(S) D(T). For compact sets , as well as for certain open sets , we investigate existence and minimal rank of bounded feedback perturbations of the form F=BE such that min.ind (T-S+F)=0 for all . Here B is a given operator from a linear space Z to Y and E is some operator from X to Z.We give a simple characterization of that situation, when such regularizing feedback perturbations exist and show that for compact sets the minimal rank never exceeds max { min.ind (T-S) }+1. Moreover, an example shows that the minimal rank, in fact, may increase from max {...} to max {...}+1, if the given B enforces a certain structure of the feedbachk perturbation F.However, the minimal rank is equal to max { min.ind (T-S) }, if is an open set such that min.ind (T-S) already vanishes for all but finitely many points . We illustrate this result by applying it to the stabilization of certain infinite-dimensional dynamical systems in Hilbert space.  相似文献   

20.
In the paper one investigates the dependence of Weyl's solution ,)=c(,)+n()s(,) of the Sturm-Liouville equation y+q()y=2y on the spectral parameter . Under the condition that the potential q is bounded from below and q()exp(c0+c[in1 ¦¦), it is proved for {ie217-01} for any positive values and A. If q()>1 and {ie217-02} for all >0, then in the semiplane >0 the Weyl solution (, ) is obtained from the Weyl solution (,x) is obtained from the Weyl solution eix with zero potential, with the aid of a generalization of B. Ya Levin's transformation operators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 184–206, 1989.I express my sincere gratitude to L. A. Pastur and I. V. Ostrovskii for valuable advice and discussions.  相似文献   

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