In abstract algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse...

In mathematical analysis, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function...

every element has a weak inverse, the semigroup is called an E-inversive or E-dense semigroup. An E-inversive semigroup may equivalently be defined by requiring...

mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying...

continuous semigroup T that satisfies ‖ T ( t ) ‖ ≤ M e ω t {\displaystyle \|T(t)\|\leq M{\rm {e}}^{\omega t}} if and only if A is closed and D(A) is dense in...

{\displaystyle S} is a semigroup/monoid generating set of G {\displaystyle G} if G {\displaystyle G} is the smallest semigroup/monoid containing S {\displaystyle...

In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such...

D(A) of the Banach space X. Then A generates a contraction semigroup if and only if D(A) is dense in X, A is dissipative, and A − λ0I is surjective for some...

{\displaystyle D(A)\cap D(B)} and forms a semigroup. Additionally, if D ( A ) ∩ D ( B ) {\displaystyle D(A)\cap D(B)} is dense in X {\displaystyle X} , the operator...

representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously been...

Markov semigroup describes the dynamics in a Markovian open quantum system. The axiomatic definition of the prototype of quantum Markov semigroups was first...

In mathematics, an analytic semigroup is particular kind of strongly continuous semigroup. Analytic semigroups are used in the solution of partial differential...

We call a subsemigroup U of a semigroup U closed if D o m S ( U ) = U {\displaystyle {\rm {{Dom}_{S}(U)=U}}} , and dense if D o m S ( U ) = S {\displaystyle...

= e A t , {\displaystyle \displaystyle {T(t)=e^{At},}} in the sense of the spectral theorem and this notation is used more generally in semigroup theory...

{\displaystyle X,} forms a regular semigroup called the semigroup of all partial transformations (or the partial transformation semigroup on X {\displaystyle X} )...

convolution semigroups arising from such a fundamental solution include the following. The heat kernel, defined by η ε ( x ) = 1 2 π ε e − x 2 2 ε {\displaystyle...

Beyond Hilbert Space (1996), appearing in Irreversibility and Causality, Semigroups and Rigged Hilbert Spaces, Arno Bohm, Heinz-Dietrich Doebner, Piotr Kielanowski...

Thus an Archimedean field is any dense ordered extension of the rationals, in the sense of any ordered field that densely embeds its rational elements. 0...

maximal cone. A similar decomposition already occurs in the semigroup. The oscillator semigroup of Roger Howe concerns the special case of this theory for...

unbounded operators. Usually A is assumed to generate a strongly continuous semigroup on the state space X. Assuming B, C and D to be bounded operators then...

states the following: If Ut is a (strongly continuous) one-parameter semigroup of unitary operators on a Hilbert space H, and P is the orthogonal projection...

makes the analogy between ring and semiring on the one hand and group and semigroup on the other hand work more smoothly. These authors often use rig for...

\\G\mapsto F+G\end{cases}}} is continuous. More generally, if S is a semigroup with the discrete topology, the operation of S can be extended to βS,...

element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0. Complements need not be...

characterizes maximally dissipative operators as the generators of contraction semigroups. A dissipative operator has the following properties: From the inequality...

on 2015-09-10. Lawson, J.; Madison, B. (1974). "Quotients of k-semigroups". Semigroup Forum. 9: 1–18. doi:10.1007/BF02194829., p. 3 Breuckmann, Tomas;...

addition operation but not a subtraction operation include commutative semigroups, commutative monoids, and semirings. Richman (1999) considers two such...

Alexei (February 2018). "Ranks of ideals in inverse semigroups of difunctional binary relations". Semigroup Forum. 96 (1): 21–30. arXiv:1612.04935. doi:10...

converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more generally,...

dissipative, thus by the spectral theorem it generates a one-parameter semigroup. A fundamental solution, also called a heat kernel, is a solution of the...