排序方式： 共有6条查询结果，搜索用时 31 毫秒
1
1.
Minimal positive operators on a Hilbert spaceH are characterized in terms of so-called parallel addition of operators. It is also shown how these operators can be used to reproduce the inverse, respectively generalized inverse, of any positive operator onH. 相似文献
2.
3.
We consider multiply hyperharmonic functions on the product space of two harmonic spaces in the sense of Constantinescu and Cornea. Earlier multiply superharmonic and harmonic functions have been studied in Brelot spaces notably by GowriSankaran. Important examples of Brelot spaces are solutions of elliptic differential equations. The theory of general harmonic spaces covers in addition to Brelot spaces also solution of parabolic differential equations. A locally lower bounded function is multiply hyperharmonic on the product space of two harmonic spaces if it is a hyperharmonic function in each variable for every fixed value of the other. We prove similar results as in Brelot spaces, but our approach is different. We study sheaf properties of multiply hyperharmonic functions. Our main theorem states that multiply hyperharmonic functions are lower semicontinuous and satisfy the axiom of completeness with respect to products of relatively compact sets. We also study nearly multiply hyperharmonic functions. 相似文献
4.
Sirkka -Liisa Eriksson-Bique Kirsti Oja-Kontio 《Advances in Applied Clifford Algebras》2001,11(2):181-189
We considerC
2-solutionsf=u+iv+jw of the system
calledH-solutions introduced by H. Leutwiler. Iff is anH-solution in ω, thenf | Ω∩ℂ is holomorphic. SinceH-solutions are real analytic, a non-zeroH-solution cannot vanish in an open subdomain of ℝ3. Our object is, by the way of examples, to show that there are many kinds of null-sets ofH-solutions in ℝ3. This is in sharp contrast to a holomorphic functionf in ℂ, where the setf
−1 ({0}) consists of discrete points only unlessf≡0.
This research is supported by the Academy of Finland 相似文献
5.
Summary Parallel addition of positive operators, a concept introduced by W. N. Anderson and R. J. Duffin [1] in connection with network theory, has already been studied by several authors. We specifically mention W. N. Anderson and G. E. Trapp [2] and [3], T. Ando [4], K. Nishio [12], E. L. Pekarev and J. L. Smul'jan [13], as well as the article [10] by the present authors.The purpose of this note is to study a generalization of parallel addition. In particular, it will be shown (Theorem 3.2) that the corresponding quasi-units, a concept introduced in [10], are again the extreme points of the convex sets, formed by the positive operators less than or equal to some fixed operator. 相似文献
6.
1