The Hausdorff dual problem for connected groups

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Connected Hausdorff subtopologies

A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable π-weight and no connected, Hausdorff subtopology is provided.

Homogeneous Countable Connected Hausdorff Spaces

In 1925, P. Urysohn gave an example of a countable connected Hausdorff space [4]. Other examples have been contributed by R. Bing [l], M. Brown [2], and E. Hewitt [3]. Relatively few of the properties of such spaces have been examined. In this paper the question of homogeneity is studied. Theorem I shows that there exists a bihomogeneous countable connected Hausdorff space. Theorems II and III ...

Connected Mappings of Hausdorff Spaces

Hausdorff-young Inequalities for Nonunimodular Groups

In this paper we deal with a definition of Lp-Fourier transform on locally compact groups. Recall that, for locally compact abelian groups, the Hausdorff-Young inequality reads: Let 1 < p < 2 and q = p/(p − 1). If g ∈ L1(G) ∩ Lp(G), then ĝ ∈ Lq(Ĝ), with ‖ĝ‖q ≤ ‖g‖p. The inequality allows to extend the Fourier transform to a continuous operator Fp : Lp → Lq by continuity. It was generalized to t...