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991.
We answer the question, when a partial order in a partially ordered algebraic structure has a compatible linear extension.
The finite extension property enables us to show, that if there is no such extension, then it is caused by a certain finite
subset in the direct square of the base set. As a consequence, we prove that a partial order can be linearly extended if and
only if it can be linearly extended on every finitely generated subalgebra. Using a special equivalence relation on the above
direct square, we obtain a further property of linearly extendible partial orders. Imposing conditions on the lattice of compatible
quasi orders, the number of linear orders can be determined. Our general approach yields new results even in the case of semi-groups
and groups. 相似文献
992.
In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression
are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space
with inner product 〈·,·〉, α is a real parameter, and φ in the rank one perturbation is a singular element belonging to
with n ≥ 3, where
is the scale of Hilbert spaces associated with L in
相似文献
993.
Yurij M. Berezansky Eugene W. Lytvynov Artem D. Pulemyotov 《Integral Equations and Operator Theory》2005,53(2):191-208
By definition, a Jacobi field
is a family of commuting selfadjoint three-diagonal operators in the Fock space
The operators J(ϕ) are indexed by the vectors of a real Hilbert space H+. The spectral measure ρ of the field J is defined on the space H− of functionals over H+. The image of the measure ρ under a mapping
is a probability measure ρK on T−. We obtain a family JK of operators whose spectral measure is equal to ρK. We also obtain the chaotic decomposition for the space L2(T−, dρ K). 相似文献
994.
Buckholtz (Proc. Amer. Math. Soc. 128 (2000), 1415–1418) gave necessary and sufficient conditions for the invertibility of the difference of two orthogonal projections in a Hilbert space. We generalize this result by investigating when the difference of such projections is a Fredholm operator, and give an explicit formula for its Fredholm inverse. 相似文献
995.
Sergio Albeverio Alexei Konstantinov Volodymyr Koshmanenko 《Integral Equations and Operator Theory》2005,52(4):455-464
The decomposition theory for the singular continuous spectrum of rank one singular perturbations is studied. A generalization of the well-known Aronszajn-Donoghue theory to the case of decompositions with respect to α-dimensional Hausdorff measures is given and a characterization of the supports of the α-singular, α-absolutely continuous, and strongly α-continuous parts of the spectral measure of
- class rank one singular perturbations is given in terms of the limiting behaviour of the regularized Borel transform. 相似文献
996.
Natasha Samko 《Integral Equations and Operator Theory》2005,51(3):417-433
For the singular integral operators with Carleman shift, preserving or changing orientation, and piecewise continuous coefficients we prove the theorem on Fredholmness and obtain the formula for index in the generalized Hölder spaces
defined by an arbitrary continuity modulus from the Bari-Stechkin class and some general weights on a closed or open finite Lyapunov curve . 相似文献
997.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
998.
In this paper we determine the topology of three-dimensional complete orientable Riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small. 相似文献
999.
Dieter Bothe 《Journal of Evolution Equations》2005,5(2):227-252
Let A be a nonlinear accretive operator in a real Banach space X and f : J × X X be continuous or of Carathéodory type, where
We investigate the existence of mild solutions of the evolution system
in case A satisfies the range condition or weaker variants thereof. This requires a careful construction of approximate solutions since m-accretivity of A is not assumed, hence associated quasi-autonomous problems need not have mild solutions. Conditions are such that additional constraints like u(t) K on J for a given closed K X are accounted for. 相似文献
1000.
In contrast to the situation in 3, where a 2-sphere with double tangent balls at each point must be tamely embedded in 3, there exist wild (n?1)-spheres in n for n>3 with this same geometric property. However, if the sphere Σ is tame moduio a subset X that lies in a polyhedron P that is tame in Σ, the dimension of P is less than n?2, n>4, and Σ has double tangent balls over X, then Σ must be tame in n. Also if the tangent balls extend over P and are pairwise congruent, the dimensional restriction on P can be dropped. Examples are given to support the necessity of the hypotheses of the included theorems. 相似文献