共查询到20条相似文献,搜索用时 31 毫秒
1.
Richard A Alò André de Korvin Vo Van Tho 《Journal of Mathematical Analysis and Applications》1977,61(1):72-96
We develop in this article a strong nonlinear integral and obtain a Riesz-type theorem (utilizing this integral) for the class of (nonlinear) Hammerstein operators. The integral is extended to the class E() of E-valued totally -measurable functions and convergence theorems are studied. Then an exchange of information is carried out between the operators and the corresponding set functions; for example, the implication of the operator being compact or unconditionally summing is drawn. In the latter case it is shown that the representing set function is analogous to strongly bounded set functions. A vast body of literature exists for both of these concepts. 相似文献
2.
If A and B are self-adjoint operators, this paper shows that A and B have order isomorphic invariant subspace lattices if and only if there are Borel subsets E and F of σ(A) and σ(B), respectively, whose complements have spectral measure zero, and there is a bijective function φ: E → F such that (i) Δ is a Borel subset of E if and only if φ(Δ) is a Borel subset of F; (ii) a Borel subset Δ of E has A-spectral measure zero if and only if φ(Δ) has B-spectral measure zero; (iii) B is unitarily equivalent to φ(A). If A is any self-adjoint operator, there is an associated function κA : ∪ {∞} → ( ∪ {0, ∞}) × {0,1} defined in this paper. If denotes the collection of all functions from ∪ {∞} into ( ∪ {0,∞}) × {0,1}, then is a parameter space for the isomorphism classes of the invariant subspace lattices of self-adjoint operators. That is, two self-adjoint operators A and B have isomorphic invariant subspace lattices if and only if κA = κB. The paper ends with some comments on the corresponding problem for normal operators. 相似文献
3.
Bruce Atkinson 《Stochastic Processes and their Applications》1983,15(2):193-201
Let p(t, x, y) be a symmetric transition density with respect to a σ-finite measure m on (E, ), g(x,y)=∫p(t,x,y)dt, and . There exists a Gaussian random field with mean 0 and covariance . Letting we consider necessary and sufficient conditions for the Markov property (MP) on sets B, C: (B), (C) c.i. given (B ∩ C). Of crucial importance is the following, proved by Dynkin: , where μB is the hitting distribution of the process corresponding to p, m with initial law μ. Another important fact is that ?μ=?ν iff μ, ν have the same potential. Putting these together with an additional transience assumption, we present a potential theoretic proof of the following necessary and sufficient condition for (MP) on sets B, C: For every x?E, TB∩C=TB+TC∮ θTB=TC+TB∮θTC a.s. Px where, for D ? , TD is the hitting time of D for the process associated with p, m. This implies a necessary condition proved by Dynkin in a recent preprint for the case where B∪C=E and B, C are finely closed. 相似文献
4.
Olav Kallenberg 《Stochastic Processes and their Applications》1979,9(2):155-161
Given a random measure η and a fixed number p>1, the Lp-intensity 6η6p of ηis defined as the total variation measure of the subadditive set function 6η(·)6p. It is shown that 6η6p can exist (be locally finite) only if the usual intensity measure Eη exists and a.s, and that in this case . If η is the conditional intensity of a simple point process ξ, then 6η6p equals the total variation of the subadditive set functions 6P[ξB = 1|Bcξ]6p and 6E[ξB|Bcξ]6p. Some applications to stochastic geometry and particle systems are discussed briefly. 相似文献
5.
Josette Coulon Jean-Louis Coulon 《Journal of Mathematical Analysis and Applications》1984,99(1):248-256
The purpose of this paper is to generalize the following situation: from the concrete structure , we define the notion of Boolean algebras; the Stone representation theorem allows us to replace the algebraic study of Boolean algebras by a topological one. Let E be a non-empty set, and J a non-empty ordered set. Note the set of all fuzzy subsets of (E,J). We shall introduce the concept of fuzzy Boolean algebra and find a representation theorem. But it will be difficult to speak of the dual fuzzy topological space of a fuzzy Boolean algebra as we shall see further, except in certain particular cases. 相似文献
6.
《Journal of Computational and Applied Mathematics》2003,158(1):49-60
Time-dependent dispersive shallow water waves in an unbounded domain are considered. The infinite domain is truncated via an artificial boundary , and a high-order non-reflecting boundary condition (NRBC) is imposed on . Then the problem is solved by a finite difference scheme in the finite domain bounded by . The sequence of NRBCs proposed by Higdon is used. However, in contrast to the original low-order implementation of the Higdon conditions, a new scheme is devised which allows the easy use of a Higdon-type NRBC of any desired order. In addition, a procedure for the automatic choice of the parameters appearing in the NRBC is proposed. The performance of the scheme is demonstrated via a numerical example. 相似文献
7.
A , denoted by (λ; t, k, v), is a system of subsets of size k from a v-set X, such that each t-subset of X is contained in exactly λ elements of . A hypergraph is a finite set Y where is a family of subsets (which we assume here are distinct) of Y such that Ei≠Ø, i?l, and ?Ei=Y. Let G be an automorphism group of where Oli is the ith orbit of l-subsets of . Let A(G; H; t, k)= (aij) be an m by n matrix, where aij is the number of copies of Oti that occur in the system of all t-subsets of all elements of Okj. Then there is a t-design with , with parameters (λ; t, k, v), and with G an automorphism groupof T iff there is an m by s submatrix M of A(G; H; t, k) where M has uniform row sums λ. The calculus for applying this theorem is illustrated and numerous t-designs for 10?v?16 are found and presented. Using a theorem of Alltop on our (12; 4, 6, 13) and (60; 4, 7, 15) we obtain a (12; 5, 7, 14) and a (60; 5, 8, 16). 相似文献
8.
Derek W Robinson 《Journal of Functional Analysis》1983,51(3):268-284
Let (, +, ∥ · ∥) denote a Banach space , ordered by a proper norm-closed convex cone +, with a Riesz norm ∥ · ∥, and define the canonical half-norm N associated with + by . The analogs of the Hille-Yosida and Feller-Miyadera-Phillips theorems characterizing the generators H of C0- or C01-semigroups S = {St}t ? 0 of positive operators, i.e., operators such that St+?+, are proved. In these theorems conditions of norm-dissipativity, e.g., are replaced by N-dissipativity, i.e., . 相似文献
9.
Milton Rosenberg 《Journal of multivariate analysis》1976,6(4):538-571
This paper is a continuation of the study made in [38]. Using Douglas' operator range theorem and Crimmins' corollary we obtain several new results on the “square-integrability of operator-valued functions with respect to a nonnegative hermitian measure”. Using these facts we are able to extend in an important way theorems on the “spectral integral of an operator-valued function” which were obtained in [38], to wit, we are able to drop assumptions that functions are closed operator-valued. We apply these results to Wiener-Masani type infinite-dimensional stationary processes, representing a purely non-deterministic process as a “moving average” and obtaining a “factorization” of its spectral density. Next, anticipating global applications of our tools, we investigate the adjoint and generalized inverse of spectral integrals. Our definition of measurability for closed-operator-valued functions plays a key role here. Finally, we partially prove a conjecture (J. Multivariate Anal. (1974), 166–209) on simpler necessary and sufficient conditions on “when is a closed densely defined operator T from q to p a spectral integral T = fΦdE?”: Let q be finite and E be of countable multiplicity for . Then (i) Tx ∈ xp each x ∈ T (T is E-subordinate), and (ii) E(B)T ? TE(B) each B ∈ (T is E-commutative) implies LxpT ? TLxq each x ∈ q (T commutes with all the cyclic projections), and thus T = fΦdE. 相似文献
10.
E.B Dynkin 《Journal of Functional Analysis》1982,47(3):381-418
This is the second paper in a series devoted to Green's and Dirichlet spaces. In the first paper, we have investigated Green's space and the Dirichlet space associated with a symmetric Markov transition function pt(x, B). Now we assume that p is a transition function of a fine Markov process X and we prove that: (a) the space can be built from functions which are right continuous along almost all paths; (b) the positive cone + in can be identified with a cone M of measures on the state space; (c) the positive cone + in can be interpreted as the cone of Green's potentials of measures μ?M. To every measurable set B in the state space E there correspond a subspace (B) of and a subspace (B) of . The orthogonal projections of onto and of onto (B) can be expressed in terms of the hitting probabilities of B by the Markov process X. As the main tool, we use additive functionals of X corresponding to measures μ?M. 相似文献
11.
J.H Michael 《Journal of Mathematical Analysis and Applications》1981,79(1):203-217
We consider the mixed boundary value problem , where Ω is a bounded open subset of n whose boundary Γ is divided into disjoint open subsets Γ+ and Γ? by an (n ? 2)-dimensional manifold ω in Γ. We assume A is a properly elliptic second order partial differential operator on and Bj, for j = 0, 1, is a normal jth order boundary operator satisfying the complementing condition with respect to A on . The coefficients of the operators and Γ+, Γ? and ω are all assumed arbitrarily smooth. As announced in [Bull. Amer. Math. Soc.83 (1977), 391–393] we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in Sobolev spaces. In fact, we construct an open subset of the reals such that, if then for is a Fredholm operator if and only if s ∈ . Moreover, = ?xewx, where the sets x are determined algebraically by the coefficients of the operators at x. If n = 2, x is the set of all reals not congruent (modulo 1) to some exceptional value; if n = 3, x is either an open interval of length 1 or is empty; and finally, if n ? 4, x is an open interval of length 1. 相似文献
12.
Let be a von Neumann algebra, let {αt}tεR be an ultraweakly continuous one-parameter group of 1-automorphisms of , and let be the set of all A such that for each ? in 1, the function t → ?(αt(A)) lies in H∞(. Then is an ultraweakly closed subalgebra of containing the identity which is proper and non-self-adjoint if {αt}tεR is not trivial. In this paper, a systematic investigation into the structure theory of is begun. Two of the more note-worthy developments are these. First of all, conditions under which is a subdiagonal algebra in , in the sense of Arveson, are determined. The analysis provides a common perspective from which to view a large number of hitherto unrelated algebras. Second, the invariant subspace structure of is determined and conditions under which is a reductive subalgebra of are found. These results are then used to produce examples where is a proper, non-self-adjoint, reductive subalgebra of . The examples do not answer the reductive algebra question, however, because although ultraweakly closed, the subalgebras are weakly dense in . 相似文献
13.
A pair (X, ) will be a t-wise balanced design (tBD) of type t?(v, K, λ) if is a family of subsets of X, called blocks, such that: (i) , where is the set of positive integers; (ii) , for every i ? I; and (iii) if T ? X, |T| = t, then there are λ ? indices i ? I where T ? Bi. Throughout this paper we make three restrictions on our tBD's: (1) there are no repeated blocks, i.e. will be a set of subsets of X; (2) t ? K or there are no blocks of size t; and (3) or does not contain all k-subsets of X for any t<k?v. Note then that X ? . Also, if we give the parameters of a specific tBD, then we will choose a minimal K.We focus on the designs with the symmetric group Sp as automorphism group, i.e. X will be the set of labelled edges of the undirected complete graph Kp and if B ? then all subgraphs of Kp isomorphic to B are also in . Call such tBD's ‘graphical tBD's’. We determine all graphical tBD's with λ = 1 or 2 which will include one with parameters 4?(15,{5,7},1). 相似文献
14.
For a closed densely defined operator T on a complex Hilbert space and a spectral measure E for of countable multiplicity q defined on a σ-algebra over an arbitrary space Λ we give three conceptually differing but equivalent answers to the question asked in the title of the paper (Theorem 1.5). We then study the simplifications which accrue when T is continuous or when q = 1 (Sect. 4). With the aid of these results we obtain necessary and sufficient conditions for T to be the integral of the spectral measure of a given group of unitary operators parametrized over a locally compact abelian group Γ (Sect. 5). Applying this result to the Hilbert space of functions which are L2 with respect to Haar measure for Γ, we derive a generalization of Bochner's theorem on multiplication operators (Sect. 6). Some results on the multiplicity of indicator spectral measures over Γ are also obtained. When Γ = we easily deduce the classical theorem about the commutant of the associated self-adjoint operator (Sect. 7). 相似文献
15.
Kenneth R Davidson 《Journal of Functional Analysis》1982,48(1):20-42
Given a commuting pair 1, 2 of abelian subalgebras of the Calkin algebra, we look for a commuting pair 1,2 of subalgebras of which project onto 1 and 2. We do not insist that i, be abelian, so i, may contain nontrivial compact operators. If X is the joint spectrum σ(1, 2), it is shown that the existence of a pair 1, 2 depends only on the element τ in Ext(X) determined by 1, 2. The set L(X) of those τ in Ext(X) which “lift” in this sense is shown to be a subgroup of Ext(X) when Ext(X) is Hausdorff, and also when i are singly generated. In this latter case, L(X) can be explicitly calculated for large classes of joint spectra. These results are applied to lift certain pairs of commuting elements of the Calkin algebra to pairs of commuting operators. 相似文献
16.
M.Ram Murty 《Journal of Number Theory》1983,16(2):147-168
Let be a family of number fields which are normal and of finite degree over a given number field K. Consider the lattice L(scF) spanned by all the elements of . The generalized Artin problem is to determine the set of prime ideals of K which do not split completely in any element H of L(scF), H≠K. Assuming the generalized Riemann hypothesis and some mild restrictions on , we solve this problem by giving an asymptotic formula for the number of such prime ideals below a given norm. The classical Artin conjecture on primitive roots appears as a special case. In another case, if is the family of fields obtained by adjoining to the q-division points of an elliptic curve E over , the Artin problem determines how often E(p) is cyclic. If E has complex multiplication, the generalized Riemann hypothesis can be removed by using the analogue of the Bombieri-Vinogradov prime number theorem for number fields. 相似文献
17.
R.A. Maller 《Stochastic Processes and their Applications》1980,10(1):65-73
We show that if Xi is a stationary sequence for which converges to a finite non zero random variable of constant sign, where Sn=X1+X2+?+Xn and Bn is a sequence of constants, then Bn is regularly varying with index 1. If in addition is finite, then is finite, and if in addition to this Xi satisfies an asymptotic independence condition, . 相似文献
18.
Jin Bai Kim 《Linear algebra and its applications》1975,10(1):69-70
Let L(E) be the set of all linear mappings of a vector space E. Let Z+ be the set of all positive integers. A nonzero element ? in L(E) is called an r-potent if . We prove that is a semigroup generated by the set of all r-potents in S(E), where r is a fixed positive integer with 2?r?n=dim(E). 相似文献
19.
J. Wolfmann 《Discrete Mathematics》1975,13(2):185-211
The notion of closure structures of finite rank is introduced and several closure structures familiar from algebra and logic are shown to be of finite rank. The following theorem is established: Let k be any natural number and any closure structure of rank k + 2. If B is a finite base (generating set) of and D is an irredundant (independent) base of such that |B| + k < |D|, then there is an irredundant base E of such that |B| < |E| < |B| + k. 相似文献
20.
Let be a family of subsets of S and let G be a graph with vertex set such that: (xA, xB) is an edge iff . The family is called a set representation of the graph G.It is proved that the problem of finding minimum k such that G can be represented by a family of sets of cardinality at most k is NP-complete. Moreover, it is NP-complete to decide whether a graph can be represented by a family of distinct 3-element sets.The set representations of random graphs are also considered. 相似文献