Norbert Youmbi - Academia.edu (original) (raw)
Papers by Norbert Youmbi
International Journal of Mathematical Analysis, 2021
This article is distributed under the Creative Commons by-nc-nd Attribution License.
A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so ... more A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in Hewitt and Ross [3]. Our main result is a proof of an extended version of Wendel's theorem for compact not necessarily commutative hypergroups.
DOAJ (DOAJ: Directory of Open Access Journals), Nov 1, 2015
In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and g... more In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and generalized Strong Law of Large Numbers (SLLN) to (graphs) groups, which she used for cryptanalysis of authentication schemes. This attack called the mean-set attack is presented here. It allows to break the Sibert authentication scheme on braid groups without solving the underlined difficult problem. We propose an amelioration to this attack and its implementation on the platform CRAG. We carry some experiments and we present the results. These results are discussed and they confirm those obtained by Mosina and Ushakov with a considerable gain of time.
A semihypergroup is defined by dropping the requirement of an identity or involution from the def... more A semihypergroup is defined by dropping the requirement of an identity or involution from the definition of a hypergroup. Dunkl [Du73] called it a hypergroup (without involution) while Jewett [Je75] referred to it as a semiconvo. In this paper, we generalize some basic algebraic results from semigroups to semihypergroups. Among other things, we define a Rees convolution product for a topological semihypergroup S and prove that if X, Y are non-empty sets and H is a hypergroup, then with the Rees convolution product, X × H × Y is a completely simple semihypergroup which has all its idempotent elements in its center. We also prove that in every locally compact semihypergroup, S, if B is a Borel subset of S then for any x ∈ S, the sets Bx − and x − B are also Borel subsets of S.
A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so ... more A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. At the center of harmonic analysis is the question of the existence of a Haar measure. The existence of a Haar measures for compact and discrete hypergroup has been done successfully. But for general hypergroup the question remain open. We put together here, work that have been done in attempts to solve this problem. Essentially we present Spector’s proof for commutative hypergroups using the more unifying definition known as DJS-definition of a hypergroup. Mathematics Subject Classification (2000). Primary 43A62.
A semihypergroup is defined by dropping the requirement of an iden-tity or involution from the de... more A semihypergroup is defined by dropping the requirement of an iden-tity or involution from the definition of a hypergroup. Dunkl [Du73] called it a hypergroup (without involution) while Jewett [Je75] referred to it as a semiconvo. In this paper, we generalize some basic algebraic results from semigroups to semihypergroups. Among other things, we define a Rees convolution product for a topological semihypergroup S and prove that if X,Y are non-empty sets and H is a hypergroup, then with the Rees convolution product, X ×H × Y is a completely simple semihypergroup which has all its idempotent elements in its center. We also prove that in every locally compact semihypergroup, S, if B is a Borel subset of S then for any x ∈ S, the sets Bx − and x−B are also Borel subsets of S.
Comput. Sci. J. Moldova, 2015
In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and g... more In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and generalized Strong Law of Large Numbers (SLLN) to (graphs) groups, which she used for cryptanalysis of authentication schemes. This attack called the mean-set attack is presented here. It allows to break the Sibert authentication scheme on braid groups without solving the underlined difficult problem. We propose an amelioration to this attack and its implementation on the platform CRAG. We carry some experiments and we present the results. These results are discussed and they confirm those obtained by Mosina and Ushakov with a considerable gain of time.
A semihypergroup is roughly speaking a locally compact Hausdorff space which has enough structure... more A semihypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Dunkl [2] called it a hypergroup (without involution) while Jewett [5] referred to it as a semiconvo. In this paper, we solve the Choquet equation on a locally compact commutative semihypergroup, and characterize idempotent measures on some classes of semihypergroups. These results generalize to semihypergroups results of [3] for semigroups. Examples are given to illustrate striking contrasts between semigroups and semihypergroups.
A semihypergroup is defined by dropping the requirement of an identity or involution from the def... more A semihypergroup is defined by dropping the requirement of an identity or involution from the definition of a hypergroup. Dunkl [Du73] called it a hypergroup (without involution) while Jewett [Je75] referred to it as a semiconvo. In this paper, we generalize some basic algebraic results from semigroups to semihypergroups. Among other things, we define a Rees convolution product for a topological semihypergroup S and prove that if X,Y are non-empty sets and H is a hypergroup, then with the Rees convolution product, X × H × Y is a completely simple semihypergroup which has all its idempotent elements in its center. We also prove that in every locally compact semihypergroup, S ,i fB is a Borel subset of S then for any x ∈ S, the sets Bx − and x − B are also Borel subsets of S.
A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so ... more A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in Hewitt and Ross [3]. Our main result is a proof of an extended version of Wendel’s theorem for compact not necessarily commutative hypergroups.
One of the central results in the theory of semigroups of operators is that the semigroup S = {T ... more One of the central results in the theory of semigroups of operators is that the semigroup S = {T (ξ) : ξ > 0} and its infinitesimal generator A are connected by an exponential formula in the form T (ξ) = eξA. Let H be a compact commutative hypergroup with dual space Ĥ. Let U = C(H) or Lp(H), it is shown that corresponding to each semigroup S = {T (ξ) : ξ > 0} of operators on U , which commutes with translations, there is a semigroup M = {Eξ : ξ > 0} of U -multipliers. Conversely a semigroup M = {Eξ : ξ > 0} of U -multipliers determines a semigroup S = {T (ξ) : ξ > 0} of operators on U , which commutes with translations. Mathematics Subject Classification: 43A62
International Journal of Mathematical Analysis
This article is distributed under the Creative Commons by-nc-nd Attribution License.
International Journal of Mathematical Analysis, 2014
Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic s... more Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic structure on a semihypergroup pause a serious challenge in extending results from semigroups. We use the notion of concretization or pseudomultiplication, to prove some results on weak convergence of the sequence of averages of convolution powers of probability measures on topological semihypergroups. As an application we provide an alternative method of solving the Choquet Equation on hypergroups.
International Journal of Mathematical Analysis, 2021
This article is distributed under the Creative Commons by-nc-nd Attribution License.
A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so ... more A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in Hewitt and Ross [3]. Our main result is a proof of an extended version of Wendel's theorem for compact not necessarily commutative hypergroups.
DOAJ (DOAJ: Directory of Open Access Journals), Nov 1, 2015
In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and g... more In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and generalized Strong Law of Large Numbers (SLLN) to (graphs) groups, which she used for cryptanalysis of authentication schemes. This attack called the mean-set attack is presented here. It allows to break the Sibert authentication scheme on braid groups without solving the underlined difficult problem. We propose an amelioration to this attack and its implementation on the platform CRAG. We carry some experiments and we present the results. These results are discussed and they confirm those obtained by Mosina and Ushakov with a considerable gain of time.
A semihypergroup is defined by dropping the requirement of an identity or involution from the def... more A semihypergroup is defined by dropping the requirement of an identity or involution from the definition of a hypergroup. Dunkl [Du73] called it a hypergroup (without involution) while Jewett [Je75] referred to it as a semiconvo. In this paper, we generalize some basic algebraic results from semigroups to semihypergroups. Among other things, we define a Rees convolution product for a topological semihypergroup S and prove that if X, Y are non-empty sets and H is a hypergroup, then with the Rees convolution product, X × H × Y is a completely simple semihypergroup which has all its idempotent elements in its center. We also prove that in every locally compact semihypergroup, S, if B is a Borel subset of S then for any x ∈ S, the sets Bx − and x − B are also Borel subsets of S.
A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so ... more A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. At the center of harmonic analysis is the question of the existence of a Haar measure. The existence of a Haar measures for compact and discrete hypergroup has been done successfully. But for general hypergroup the question remain open. We put together here, work that have been done in attempts to solve this problem. Essentially we present Spector’s proof for commutative hypergroups using the more unifying definition known as DJS-definition of a hypergroup. Mathematics Subject Classification (2000). Primary 43A62.
A semihypergroup is defined by dropping the requirement of an iden-tity or involution from the de... more A semihypergroup is defined by dropping the requirement of an iden-tity or involution from the definition of a hypergroup. Dunkl [Du73] called it a hypergroup (without involution) while Jewett [Je75] referred to it as a semiconvo. In this paper, we generalize some basic algebraic results from semigroups to semihypergroups. Among other things, we define a Rees convolution product for a topological semihypergroup S and prove that if X,Y are non-empty sets and H is a hypergroup, then with the Rees convolution product, X ×H × Y is a completely simple semihypergroup which has all its idempotent elements in its center. We also prove that in every locally compact semihypergroup, S, if B is a Borel subset of S then for any x ∈ S, the sets Bx − and x−B are also Borel subsets of S.
Comput. Sci. J. Moldova, 2015
In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and g... more In her thesis, Mosina introduced the concept of mean-set of random (graph-) group-variables and generalized Strong Law of Large Numbers (SLLN) to (graphs) groups, which she used for cryptanalysis of authentication schemes. This attack called the mean-set attack is presented here. It allows to break the Sibert authentication scheme on braid groups without solving the underlined difficult problem. We propose an amelioration to this attack and its implementation on the platform CRAG. We carry some experiments and we present the results. These results are discussed and they confirm those obtained by Mosina and Ushakov with a considerable gain of time.
A semihypergroup is roughly speaking a locally compact Hausdorff space which has enough structure... more A semihypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Dunkl [2] called it a hypergroup (without involution) while Jewett [5] referred to it as a semiconvo. In this paper, we solve the Choquet equation on a locally compact commutative semihypergroup, and characterize idempotent measures on some classes of semihypergroups. These results generalize to semihypergroups results of [3] for semigroups. Examples are given to illustrate striking contrasts between semigroups and semihypergroups.
A semihypergroup is defined by dropping the requirement of an identity or involution from the def... more A semihypergroup is defined by dropping the requirement of an identity or involution from the definition of a hypergroup. Dunkl [Du73] called it a hypergroup (without involution) while Jewett [Je75] referred to it as a semiconvo. In this paper, we generalize some basic algebraic results from semigroups to semihypergroups. Among other things, we define a Rees convolution product for a topological semihypergroup S and prove that if X,Y are non-empty sets and H is a hypergroup, then with the Rees convolution product, X × H × Y is a completely simple semihypergroup which has all its idempotent elements in its center. We also prove that in every locally compact semihypergroup, S ,i fB is a Borel subset of S then for any x ∈ S, the sets Bx − and x − B are also Borel subsets of S.
A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so ... more A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in Hewitt and Ross [3]. Our main result is a proof of an extended version of Wendel’s theorem for compact not necessarily commutative hypergroups.
One of the central results in the theory of semigroups of operators is that the semigroup S = {T ... more One of the central results in the theory of semigroups of operators is that the semigroup S = {T (ξ) : ξ > 0} and its infinitesimal generator A are connected by an exponential formula in the form T (ξ) = eξA. Let H be a compact commutative hypergroup with dual space Ĥ. Let U = C(H) or Lp(H), it is shown that corresponding to each semigroup S = {T (ξ) : ξ > 0} of operators on U , which commutes with translations, there is a semigroup M = {Eξ : ξ > 0} of U -multipliers. Conversely a semigroup M = {Eξ : ξ > 0} of U -multipliers determines a semigroup S = {T (ξ) : ξ > 0} of operators on U , which commutes with translations. Mathematics Subject Classification: 43A62
International Journal of Mathematical Analysis
This article is distributed under the Creative Commons by-nc-nd Attribution License.
International Journal of Mathematical Analysis, 2014
Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic s... more Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic structure on a semihypergroup pause a serious challenge in extending results from semigroups. We use the notion of concretization or pseudomultiplication, to prove some results on weak convergence of the sequence of averages of convolution powers of probability measures on topological semihypergroups. As an application we provide an alternative method of solving the Choquet Equation on hypergroups.