The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fi...The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fields, and as well as weakly harmonizable random fields of S1 and S2 into Hilbert spaces.展开更多
A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact...A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact groupoid is given. This is used in order to extend some well-known results from locally compact groups to the case of locally compact groupoids. Indeed, we have proved that if L is a continuous irreducible representation of a compact groupoid G defined by a continuous Hilbert bundle H = （Hu）u∈G^0, then each Hu is finite dimensional. It is also shown that if L is an irreducible representation of a principal locally compact groupoid defined by a Hilbert bundle （G^0, （Hu）,μ）, then dimHu = 1 （u ∈ G^0）. Furthermore it is proved that every square integrable representation of a locally compact groupoid is unitary equivalent to a subrepresentation of the left regular representation. Furthermore, for r-discrete groupoids, it is shown that every irreducible subrepresentation of the left regular representation is square integrable.展开更多
In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. I...In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. Indeed, we have improved compact groups to the general setting of locally a well-krown result of Bhatt and Dedania from locally compact hypergroups.展开更多
基金the Research Project No. 830104the Center of Excellence for Mathematics of the University of Isfahan for their financial supports
文摘The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fields, and as well as weakly harmonizable random fields of S1 and S2 into Hilbert spaces.
基金Supported by the office of Graduate Studies and the Center of Excellence for Mathematics of the University of Isfahan
文摘A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact groupoid is given. This is used in order to extend some well-known results from locally compact groups to the case of locally compact groupoids. Indeed, we have proved that if L is a continuous irreducible representation of a compact groupoid G defined by a continuous Hilbert bundle H = （Hu）u∈G^0, then each Hu is finite dimensional. It is also shown that if L is an irreducible representation of a principal locally compact groupoid defined by a Hilbert bundle （G^0, （Hu）,μ）, then dimHu = 1 （u ∈ G^0）. Furthermore it is proved that every square integrable representation of a locally compact groupoid is unitary equivalent to a subrepresentation of the left regular representation. Furthermore, for r-discrete groupoids, it is shown that every irreducible subrepresentation of the left regular representation is square integrable.
基金both The Research Affairs (Research Project No.850709)The Center of Excellence for Mathematics of the University of Isfahan
文摘In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. Indeed, we have improved compact groups to the general setting of locally a well-krown result of Bhatt and Dedania from locally compact hypergroups.
