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1.
Let U be a subharmonic function in C with a Riesz mass , distributed on the negative semiaxis without some neighborhood of zero, let and be its order and lower order, and let B(r, U) be the maximum of U(z) for ¦z¦=r. Estimates are obtained for the measure of sets of those values of r 0 for which certain inequalities hold. The following result is typical. LetE = {r:u(re l)–cosB<(r,U) > 0}. If < < 1, ¦¦=., then the lower logarithmic density of the set E is at least 1 – /. If < > 1,¦¦ ., then the upper logarithmic density of the set E is at least 1 – /.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 31–38, 1988.  相似文献   

2.
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   

3.
Let V: R N [0, ] be a measurable function, and >0 be a parameter. We consider the behaviour of the spectral bound of the operator 1/2–V as a function of . In particular, we give a formula for the limiting value as , in terms of the integrals of V over subsets of R N on which the Laplacian with Dirichlet boundary conditions has prescribed values. We also consider the question whether this limiting value is attained for finite .  相似文献   

4.
Let a selfadjoint operator-valued functionL() be given on the interval [a,b] such thatL(a)0,L(b)0,L()0 (ab), andL() has a certain smoothness (for instance, it satisfies Hölder's condition). It turns out that the spectral theory of the operator-valued functionL() can be reduced to the spectral theory of one operatorZ, the spectrum of which lies on (a, b) and which is similar to a selfadjoint operator. In particular, the factorization takes place:L()=M()(I–Z), where the operator-valued functionM() is invertible on [a, b]. Earlier similar results were known only for analytic operator-valued functions. The authors had to use new methods for the proof of the described theorem. The key moment is the decomposition ofL –1() into the sume of its principal and regular parts.  相似文献   

5.
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   

6.
In a Minkowski space with unit ballS, a setD() is diametrically complete ifD()={. In this paper a method is given for generating such setsD() which contain an arbitrary setX. This technique is then employed to find necessary and sufficient conditions for a setA to lie on the boundary of some suchD() and bounds are given on the acceptable values of .  相似文献   

7.
There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues 12 n if and only if, 1 + n 0, 2 + n-10,..., m + n - m + 10, m + 10,..., n - m 0, in which m is the matching numberof G. Other observations are also made about the symmetric nonnegative inverse eigenvalue problem with respect to a graph  相似文献   

8.
We study (s, k, 1, 2)-translation divisible designs with 10 in the singular and semi-regular case. Precisely, we describe singular (s, k, 1, 2)-TDD's by quasi-partitions of suitable quotient groups or subgroups of their translation groups. For semi-regular (s, k, 1, 2)-TDD's (and, more general, for the case 2>1) we prove that their translation groups are either Frobenius groups or p-groups of exponent p. Some examples are given for the singular, semi-regular and regular case.  相似文献   

9.
Summary In this paper, we study oscillatory stochastic integrals of the form where is a non zero parameter andg a square integrable function. We study integrability properties of () and its behavior as a function of , using stochastic calculus techniques: martingale theory, representation of Itô for a random variable of the Wiener space, lemma of Garsia-Rodemich-Rumsey .... We also obtain limit theorems in law related to the variables () based upon an asymptotic version of a theorem of Knight on orthogonal continuous martingales.We consider the random measure, image by the Brownian motion of the unbounded measure 1[0,] (s)g(s) ds; we prove the existence and the continuity of an occupation time density.Finally, under a stronger integrability condition ong, we show the existence of a density for the law of (), using Malliavin's calculus.  相似文献   

10.
We study the minimality of elementsx h,j,k of canonical systems of root vectors. These systems correspond to the characteristic numbers k of operator functionsL() analytic in an angle; we assume that operators act in a Hilbert space . In particular, we consider the case whereL()=I+T()c, >0,I is an identity operator,C is a completely continuous operator, (I- C)–1c for ¦arg¦, 0<<, the operator functionT() is analytic, and T()c for ¦arg¦<. It is proved that, in this case, there exists >0 such that the system of vectorsC v x h,j,k is minimal in for arbitrary positive <1+, provided that ¦k¦>.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 545–566, May, 1994.This research was partially supported by the Ukrainian State Committee of Science and Technology.  相似文献   

11.
Letk and be positive integers, andG a 2-connected graph of ordern with minimum degree and independence number. A cycleC ofG is called aD -cycle if every component ofG – V(C) has order smaller than. The graphG isk-cyclable if anyk vertices ofG lie on a common cycle. A previous result of the author is that if k 2, G isk-connected and every connected subgraphH ofG of order has at leastn +k 2 + 1/k + 1 – vertices outsideH adjacent to at least one vertex ofH, thenG contains aD -cycle. Here it is conjectured that k-connected can be replaced by k-cyclable, and this is proved fork = 3. As a consequence it is shown that ifn 4 – 6, or ifG is triangle-free andn 8 – 10, thenG contains aD 3-cycle orG , where denotes a well-known class of nonhamiltonian graphs of connectivity 2. As an analogue of a result of Nash-Williams it follows that ifn 4 – 6 and – 1, thenG is hamiltonian orG . The results are all best possible and compare favorably with recent results on hamiltonicity of graphs which are close to claw-free.  相似文献   

12.
Let L() be an entire function of exponential type with simple zeros 1, 2, ...; let ¯D be the smallest closed convex set which contains all of the singularities of the function which is associated with L() in the sense of Borel. In [1] there are necessary and sufficient conditions on L() under which a function f(z) which is analytic in ¯D can be represented in D by a Dirichlet series with exponents 1, 2, ... We obtain new equivalent conditions on L().Translated from Matematicheskie Zametki, Vol. 20, No. 1, pp. 91–104, July, 1976.  相似文献   

13.
We consider a selfadjoint and smooth enough operator-valued functionL() on the segment [a, b]. LetL(a)0,L(b)0, and there exist two positive numbers and such that the inequality |(L()f, f)|< ([a, b] f=1) implies the inequality (L'()f, f)>. Then the functionL() admits a factorizationL()=M()(I-Z) whereM() is a continuous and invertible on [a, b] operator-valued function, and operatorZ is similar to a selfadjoint one. This result was obtained in the first part of the present paper [10] under a stronge conditionL()0 ( [a,b]). For analytic functionL() the result of this paper was obtained in [13].  相似文献   

14.
We characterize the relationship between the space L1() and the dual L1() of the space L1(), where (, ) is a dual pair of vector measures with associated spaces of integrable functions L1() and L1() respectively. Since the result is rather restrictive, we introduce the notion of range duality in order to obtain factorizations of operators from Banach function spaces that are dominated by the integration map associated to the vector measure . We obtain in this way a generalization of the Grothendieck-Pietsch Theorem for p-summing operators.*The research was partially supported by MCYT DGI project BFM 2001-2670.**The research was partially supported by MCYT DGI project BFM 2000-1111.  相似文献   

15.
LetH=(A, B) be a pair of HermitianN×N matrices. A complex number is an eigenvalue ofH ifdet(A–B)=0 (we include = ifdetB=0). For nonsingularH (i.e., for which some is not an eigenvalue), we show precisely which eigenvalues can be characterized as k + =sup{inf{*A:*B=1,S},SS k},S k being the set of subspaces of C N of codimensionk–1.Dedicated to the memory of our friend and colleague Branko NajmanResearch supported by NSERC of Canada and the I.W.Killam FoundationProfessor Najman died suddenly while this work was at its final stage. His research was supported by the Ministry of Science of CroatiaResearch supported by NSERC of Canada  相似文献   

16.
Consider a functionL() defined on an interval of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point 0 and a vector 0 H( 0 0) are called eigenvalue and eigenvector ofL() ifL() ifL(0) 0 = 0. Supposing that the functionL() can be represented as an absolutely convergent Fourier integral, the interval is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL() corresponding to the eigenvalues from the interval form an unconditional basis in the subspace spanned by them.  相似文献   

17.
We have obtained an estimate, in terms of partial and mixed moduli, of the continuity of deviation of the Cesáro (C, ) means ( = (1,...,n),i , 1 > –1, ) of the sequence of rectangular partial sums ofn-multiple (n>1) conjugate trigonometric series from then-multiple truncated conjugate function. This estimate implies the result on them -convergence (1) of (C, ) means (1 > 0, ) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that them -convergence cannot be replaced by ordinary convergence.  相似文献   

18.
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   

19.
A sequence {A } of linear bounded operators is called stable if, for all sufficiently large , the inverses of A exist and their norms are uniformly bounded. We consider the stability problem for sequences of Toeplitz operators {T(k a)}, where a(t) is an almost-periodic function on unit circle and k a is an approximate identity. A stability criterion is established in terms of the invertibility of a family of almost-periodic functions. This family of functions depends on the approximate identity used in a very subtle way, and the stability condition is, in general, stronger than the invertibility condition of the Toeplitz operator T(a).  相似文献   

20.
As in [N], [LN] the Newton diagram is used in order to get information about the first terms of the Puiseux expansions of the eigenvalues () of the perturbed matrix pencilT(, )=A()+B(, ) in the neighbourhood of an unperturbed eigenvalue () ofA(). In fact sufficient conditions are given which assure that the orders of these first terms correspond to the partial multiplicities of the eigenvalue 0 ofA().  相似文献   

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