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...erms of [[partial permutation]]s. It also has a [[denotational semantics]] in which [[formula (logic)|formula]]s are interpreted by [[module (algebra)|mo ==Noncommutativity in logic== ...

...iption|Theory allowing one to apply mathematical functions to mathematical operators}} ...types of [[functional equations]], or in logic for systems of [[predicate calculus]].) ...

...inorm|seminorms]] of the form <math>T\mapsto\|Tx\|</math>, as ''x'' varies in ''H''. ...uation map <math>T\mapsto Tx</math> (taking values in ''H'') is continuous in T. The equivalence of these two definitions can be seen by observing that a ...

{{Short description|Linear operator in mathematics}} ...ition operator''' <math>C_\phi</math> with symbol <math>\phi</math> is a [[linear operator]] defined by the rule ...

{{About|operators in mathematics|other uses|Operator (disambiguation)}} ...of an operator is often difficult to characterize explicitly (for example in the case of an [[integral operator]]), and may be extended so as to act on ...

...rightarrow \mathbb{K}[x]</math> on the [[vector space]] of [[polynomial]]s in a variable <math>x</math> over a [[field (mathematics)|field]] <math>\mathb In other words, if <math>f</math> is a "shift" of <math>g</math>, then <math>Q ...

*[[Bounded linear operator]] **[[Continuous linear extension]] ...

{{Short description|Type of derivative of a linear operator}} ...eratorname{End}(\mathbb{K}[x])</math>. That is, <math>T'</math> is another linear operator <math>T': \mathbb{K}[x] \to \mathbb{K}[x]</math> ...

...rs may be presented abstractly by their characteristics, such as [[bounded linear operator]]s or [[closed operator]]s, and consideration may be given to [[no If a collection of operators forms an [[algebra over a field]], then it is an [[operator algebra]]. The ...

{{Short description|Technique in mathematics}} {{further|Frobenius covariant|Holomorphic functional calculus}} ...

.../sup> to ''T'' yields the operator ''T''². Using the functional calculus for larger classes of functions, we can for example define rigorously the " ...l calculus]], and its focus is different than the [[holomorphic functional calculus]]. ...

{{short description|Linear mathematical operator which translates a function}} {{About|shift operators in mathematics|operators in computer programming languages|Bit shift|the shift operator of group scheme ...

...ematical models that include ultrametric [[pseudo-differential equations]] in a [[Archimedean property|non-Archimedean]] space. The study of pseudo-differential operators began in the mid 1960s with the work of [[Joseph J. Kohn|Kohn]], [[Louis Nirenberg|N ...

{{Calculus|expanded=Specialized calculi}} In [[fractional calculus]], an area of [[mathematical analysis]], the '''differintegral''' is a comb ...

...from a general operator. In particular, the spectral properties of compact operators resemble those of square matrices. ...from the matrix case before discussing the spectral properties of compact operators. The reader will see that most statements transfer verbatim from the matrix ...

...ntegers]] <math display="inline">\left\{0, 1, 2, 3, \ldots \right\}</math> in which the index of each polynomial equals its [[Degree of a polynomial|degr ...l sequences put on firm footing the vague 19th century notions of [[umbral calculus]]. ...

...'''modal μ-calculus''' ('''Lμ''', '''L_μ''', sometimes just '''μ-calculus''', although this can have a more general meaning) is an extension of [[pro ...n the μ-calculus, including [[CTL*]] and its widely used fragments&mdash;[[linear temporal logic]] and [[computational tree logic]].<ref>Clarke p.108, Theore ...

{{Short description|Mathematical notation}}{{Calculus|expanded=Multivariable calculus}} ...[[mathematical notation]] that simplifies formulas used in [[multivariable calculus]], [[partial differential equation]]s and the theory of [[distribution (mat ...

* [[Logical operator]] or logical connective in mathematical logic ** [[Linear operator]] ...

In [[mathematics]], in the area of [[combinatorics]] and [[quantum calculus]], the '''''q''-derivative''', or '''Jackson derivative''', is a [[q-analog Formally, in terms of Lagrange's [[shift operator]] in logarithmic variables, it amounts to the operator ...