排序方式: 共有27条查询结果,搜索用时 453 毫秒
1.
Let be a -group with generator , and let be a local -semigroup commuting with . Then the operators , , form a local -semigroup. It is proved that if is injective and is the generator of , then is closable and is the generator of . Also proved are a characterization theorem for local -semigroups with not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem:
2.
Sen-Yen Shaw 《Journal of Functional Analysis》1982,49(2):152-169
The aim of this paper is to study ergodic properties (i.e., properties about the limit of Cesàro averages) of a semigroup of bounded linear operators on a Banach space X, which is assumed to be continuous and locally integrable in the sense of a certain general weak topology of X. Then the results are applied to particular examples, such as locally strongly integrable semigroups, their dual semigroups, and the tensor product semigroup of two (C0)-semigroups. 相似文献
3.
4.
Jung-Chan Chang Sen-Yen Shaw 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1670-1683
In this paper, we investigate the existence, uniqueness of solutions to boundary Cauchy equations with infinite delay, which are more general than the previous studies. The conclusions are applied to an age dependent population with delay in the birth process. 相似文献
5.
Peculiar properties of hermitian and positive n-times integrated C-cosine functions on Banach spaces are investigated. Among them are: (1) Any nondegenerate positiven -times integrated C-cosine function is infinitely differentiable in operator norm; (2) An exponentially bounded, nondegenerateC -cosine function on L
p
() (1
L 1(), C0 , in case C has dense range) is positive if and only if its generator is bounded, positive, and commutes with C. 相似文献
6.
Chui HC Shaw SY Ko MS Liu YW Shy JT Lin T Cheng WY Roussev RV Fejer MM 《Optics letters》2005,30(6):646-648
The iodine molecule has frequently been used as a frequency reference from the green to the near-infrared wavelength region (500-900 nm). We describe the frequency locking of the second-harmonic signal of a 197.2-THz (1520.25-nm) distributed-feedback diode laser to the absorption lines of the iodine hyperfine structure; a frequency jitter below 0.1 MHz was achieved at a 300-ms time constant. This scheme provides a simple, compact, and high-performance frequency reference in the optical communication band. 相似文献
7.
We estimate pointwise convergence rates of approximation for functions with derivatives of bounded variation and for functions which are exponentially bounded and have derivatives locally of bounded variation. The approximation is made through the operation of a sequence of integral operators with not necessarily positive kernel functions. The general result is then applied to deduce estimates for Beta operators, Hermite-Fejér operators, Picard operators, Gauss-Weierstrass operators, Baskakov operators, Mirakjan-Szász operators, Bleimann-Butzer-Hahn operators, Phillips operators, and Post-Widder operators. 相似文献
8.
We discuss relations among notions of (C,1)-convergence, almost-convergence, absolute almost-convergence, and -convergence of a continuous vector-valued function f(t) as t tends to infinity. Equivalent conditions and Tauberian criterions are obtained, and some examples are exhibited. 相似文献
9.
It is first observed that a uniformly bounded cosine operator function C() and the associated sine function S() are totally non-stable. Then, using a zero-one law for the Abel limit of a closed linear operator, we prove some results concerning strong mean stability and uniform mean stability of C(). Among them are: (1) C() is strongly (C,1)-mean stable (or (C,2)-mean stable, or Abel-mean stable) if and only if 0ρ(A)σc(A); (2) C() is uniformly (C,2)-mean stable if and only if S() is uniformly (C,1)-mean stable, if and only if , if and only if , if and only if C() is uniformly Abel-mean stable, if and only if S() is uniformly Abel-mean stable, if and only if 0ρ(A). 相似文献
10.
Sen-Yen Shaw 《Journal of Mathematical Analysis and Applications》1980,76(2):432-439
Let etSande?tT be (C0)-semigroups on a Banach space X. Their tensor product (t) is defined by (t)A = etSAetT (A?B(X)) and has the generator Δ formally of the form ΔA = SA ? AT. Under the assumption that {(t); t ? 0} is bounded, we investigate the Abel limit and the Cesàro limit of (t)A at ∞. If denotes the set of operators A for which the Abel limit Ps(A) [resp. Pu(A)] exists in the strong [resp. uniform] operator topology, then and the limit defines a projection Ps[Pu] from [resp. ] onto N(Δ) with N(Δ) with . If, in addition, S and T are Hilbert space normal operators such that gq(S) ∩ gq(T) ≠ φ, then contains all compact operators. 相似文献