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Linearization technique for nonlinear differential systems
the differential system. Carleman linearization may be regarded as a systematic extension of the usual local linearization of nonlinear differential
Carleman_linearization
Swedish mathematician
Ivar Fredholm, and Bernard Koopman, he devised the Carleman embedding (also called Carleman linearization), a way to embed a finite-dimensional system of
Torsten_Carleman
later introduced Riordan arrays. They are also related to Carleman linearization and Carleman (embedding) matrices. Grunsky matrices can be expressed with
Jabotinsky_matrix
M=\{M_{k}\}_{k=0}^{\infty }} be a sequence of positive real numbers. Then the Denjoy–Carleman class of functions CM([a,b]) is defined to be those f ∈ C∞([a,b]) which
Quasi-analytic_function
In functional analysis, the Hilbert–Carleman determinant is an operator determinant for certain integral operators on Banach spaces, whose kernels are
Hilbert–Carleman_determinant
Linear operator in mathematics
operator. Jabotinsky matrix Carleman linearization Composition ring – Algebraic structure Multiplication operator – Linear operator scaling by a fixed
Composition_operator
Carleman's inequality is an inequality in mathematics, named after Torsten Carleman, who proved it in 1923 and used it to prove the Denjoy–Carleman theorem
Carleman's_inequality
Quantum algorithm for solving systems of linear equations
equations. Liu et al. utilized Carleman linearization for second order equations and Lloyd et al. used a mean field linearization method inspired by the nonlinear
HHL_algorithm
Optimization process
(2015). "Fast Moving Horizon Estimation of nonlinear processes via Carleman linearization". 2015 American Control Conference (ACC). pp. 3379–3385. doi:10
Moving_horizon_estimation
inequality Borell–Brascamp–Lieb inequality Brezis–Gallouet inequality Carleman's inequality Carlson's inequality Chebyshev–Markov–Stieltjes inequalities
List_of_inequalities
Measure of the shape of a function
\alpha _{k}=E\left[X^{k}\right]} it is sufficient, for example, that Carleman's condition be satisfied: ∑ k = 1 ∞ 1 α 2 k 1 / 2 k = ∞ {\displaystyle \sum
Moment_(mathematics)
problem — find N points on a sphere that minimize some kind of energy Carleman's condition — condition guaranteeing that a measure is uniquely determined
List of numerical analysis topics
List_of_numerical_analysis_topics
Danskin's theorem (convex analysis) Darboux's theorem (real analysis) Denjoy–Carleman theorem (functional analysis) Denjoy–Young–Saks theorem (real analysis)
List_of_theorems
order α = 1 + 1 ω . {\displaystyle \alpha =1+{\frac {1}{\omega }}.} Denjoy–Carleman theorem Gevrey, Maurice (1918). "Sur la nature analytique des solutions
Gevrey_class
Trying to map moments to a measure that generates them
μ {\textstyle \mu _{n}\rightarrow \mu } in distribution. By checking Carleman's condition, we know that the standard normal distribution is a determinate
Moment_problem
of holomorphy is that of [Fantappié, 1930-33]. Many classes of Denjoy Carleman ultradifferentiable functions, both of Beurling type and of Roumieu-type
Convenient_vector_space
{\displaystyle u_{t}+2\kappa u_{x}-u_{xxt}+3uu_{x}=2u_{x}u_{xx}+uu_{xxx}\,} Peakons Carleman 1+1 u t + u x = v 2 − u 2 = v x − v t {\displaystyle \displaystyle
List of nonlinear partial differential equations
List_of_nonlinear_partial_differential_equations
Mathematical compact operator
non-zero real eigenvalues λn satisfy the following identities proved by Carleman (1921): t r K 2 = ∑ λ n 2 , det ( I − z K 2 ) = ∏ n = 1 ∞ ( 1 − z λ n 2
Symmetrizable compact operator
Symmetrizable_compact_operator
Science of Georgian SSR, Tbilisi, 1965 (Russian). Džanašija, G. A. (1962). "Carleman's problem for the class of Gevrey functions". Doklady Akademii Nauk SSSR
Gigla_Janashia
Result of repeatedly applying a mathematical function
S2CID 119675869. Berkolaiko, G.; Rabinovich, S.; Havlin, S. (1998). "Analysis of Carleman Representation of Analytical Recursions". J. Math. Anal. Appl. 224: 81–90
Iterated_function
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