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Look up resolvent in Wiktionary, the free dictionary. In mathematics, resolvent meaning "that which resolves" may refer to: Resolvent formalism in operator...

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

In Galois theory, a discipline within the field of abstract algebra, a resolvent for a permutation group G is a polynomial whose coefficients depend polynomially...

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...

becomes finding the roots of the resolvent cubic which is done elsewhere. This resolvent cubic is equivalent to the resolvent cubic given above (equation (1a))...

completeness. The clause produced by a resolution rule is sometimes called a resolvent. The resolution rule in propositional logic is a single valid inference...

In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four: P ( x )...

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...

as 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...

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

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...

Liouville–Neumann series is a function series that results from applying the resolvent formalism to solve Fredholm integral equations in Fredholm theory. The...

if 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 )...

discriminant of P then X 2 − D {\displaystyle X^{2}-D} is a resolvent for the alternating group. This resolvent is always separable (assuming the characteristic...

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...

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 (...

{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...

Fredholm operator Fredholm solvability Fredholm's theorem Fredholm theory Resolvent formalism Awards Björkénska priset (1910) Scientific career Fields Mathematics...

alternative way of deriving the quadratic formula is via the method of Lagrange resolvents, which is an early part of Galois theory. This method can be generalized...

precisely the same way as for bounded operators: λ is a spectral value if the resolvent operator R λ = ( T − λ ) − 1 {\displaystyle R_{\lambda }=(T-\lambda )^{-1}}...