theory, the resolvent set of a linear operator is a set of complex numbers for which the operator is in some sense "well-behaved". The resolvent set plays an...

theory Resolvent set in operator theory, the set of points where an operator is "well-behaved" Feller process § Resolvent in probability theory Resolvent (Galois...

In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach...

denoted σ ( T ) {\displaystyle \sigma (T)} , and its complement, the resolvent set, is denoted ρ ( T ) = C ∖ σ ( T ) {\displaystyle \rho (T)=\mathbb {C}...

a bounded operator) is called the resolvent of T. The spectrum of T is therefore the complement of the resolvent set of T in the complex plane. Every eigenvalue...

differentiability can be made regarding the resolvent map. The resolvent set ρ(T) is actually an open set on which the resolvent map is analytic. This property will...

A is closed and D(A) is dense in X, every real λ > ω belongs to the resolvent set of A and for such λ and for all positive integers n, ‖ ( λ I − A ) −...

in terms of the resolvent operator of the generator: all λ with positive real part belong to the resolvent set of A and the resolvent operator is uniformly...

complement of the spectrum σ ( T ) {\displaystyle \sigma (T)} is known as resolvent set ρ ( T ) {\displaystyle \rho (T)} that is ρ ( T ) = C ∖ σ ( T ) {\displaystyle...

A:\operatorname {Dom} (A)\to H} be an unbounded operator. The resolvent set (or regular set) of A {\displaystyle A} is defined as ρ ( A ) = { λ ∈ C : ∃...

\setminus \sigma _{\mathrm {ess} ,1}(T)} that do not intersect with the resolvent set C ∖ σ ( T ) {\displaystyle \mathbb {C} \setminus \sigma (T)} . Each...

need for explicit representation of the resolvents. This description of the resolution technique uses a set S as the underlying data-structure to represent...

region G Γ {\displaystyle G_{\Gamma }} and lies entirely within the resolvent set ρ ( A ) {\displaystyle \rho (A)} ( Γ ⊂ ρ ( A ) {\displaystyle \Gamma...

If we set U = u2, then solving this equation becomes finding the roots of the resolvent cubic which is done elsewhere. This resolvent cubic is equivalent...

maximally dissipative case.) In that case one has (0, ∞) ⊂ ρ(A) (the resolvent set of A). A is a closed operator if and only if the range of λI - A is...

of choosing the "correct" resolvent of a linear operator at the essential spectrum based on the behavior of the resolvent near the essential spectrum...

half-plane Re(λ) > ω is contained in the resolvent set of A and, moreover, there is a constant C such that for the resolvent R λ ( A ) {\displaystyle R_{\lambda...

holomorphic in a disc centered at the origin. In case 1/z belongs to the resolvent set of A (which is the case on a possibly smaller disc centered at the origin)...

{1}{K-\omega }}f.} A solution of this form is referred to as the resolvent formalism, where the resolvent is defined as the operator R ( ω ) = 1 K − ω I . {\displaystyle...

sequence. Consensus theorem, an identity in Boolean algebra. Consensus or resolvent term, defined in the consensus theorem. Scientific consensus, the collective...

specific quintic is solvable in radicals can be done by using Cayley's resolvent. This is a univariate polynomial of degree six whose coefficients are...

method, Glasser's method, and the Cockle–Harley method of differential resolvents described below. An alternative form is obtained by setting u = v d 1...

Galois theory, this can also be understood in terms of Lagrange resolvents. The resolvent of a quintic is of degree 6—this corresponds to an exotic inclusion...

series is used in functional analysis. It is closely connected to the resolvent formalism for studying the spectrum of bounded operators and, applied...

1070/RM2004v059n01ABEH000698. MR 2068840. Farb, Benson; Wolfson, Jesse (2020). "Resolvent degree, Hilbert's 13th Problem and geometry". L'Enseignement mathématique...

= Ker(λi − A)m+1. Furthermore, the poles of the resolvent function ζ → (ζ − A)−1 coincide with the set of eigenvalues of A. Theorem — Let X be a Banach...

52 which both share some common subformula p {\displaystyle p} . The resolvent is formed as the disjunction of E {\displaystyle E} , with p {\displaystyle...

by first-order resolution, because the resolvent of two Horn clauses is itself a Horn clause, and the resolvent of a goal clause and a definite clause...

rational coefficients or the polynomial P2 − 1024 z Δ, named Cayley's resolvent, has a rational root in z, where P = z 3 − z 2 ( 20 r + 3 p 2 ) − z (...

{\displaystyle S_{4}\to S_{3}} corresponds to the resolvent cubic, in terms of Lagrange resolvents. In the construction of finite rings, eight of the...