Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2014, Volume 16, Issue 6, pp. 1350044 - 1-1350044-15

The Lie–Trotter–Kato product formula has been recently extended into Hadamard spaces by Stojkovic...

Lie-Trotter-Kato formula | Hadamard space | weak convergence | resolvent | Gradient flow semigroup | NONLINEAR MARKOV OPERATORS | CONVEX FUNCTIONALS | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | HILBERT BALL | SINGULAR SPACES | PROXIMAL POINT ALGORITHM | MATHEMATICS | SEMIGROUPS | PRODUCT FORMULA | MANIFOLDS | Approximation | Functionals | Mathematical analysis | Curved | Proving | Convergence | Mathematics - Functional Analysis

Lie-Trotter-Kato formula | Hadamard space | weak convergence | resolvent | Gradient flow semigroup | NONLINEAR MARKOV OPERATORS | CONVEX FUNCTIONALS | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | HILBERT BALL | SINGULAR SPACES | PROXIMAL POINT ALGORITHM | MATHEMATICS | SEMIGROUPS | PRODUCT FORMULA | MANIFOLDS | Approximation | Functionals | Mathematical analysis | Curved | Proving | Convergence | Mathematics - Functional Analysis

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 427, Issue 2, pp. 190 - 196

In this paper we present a class of Lie–Trotter formulae for Hermitian operators including the formulae derived by Hiai–Petz and Furuta. A Lie...

Lie–Trotter formula | Log-Euclidean mean | Sagae–Tanabe mean | Geometric mean | Positive definite operator | Spectral geometric mean | Lie-Trotter formula | Sagae-Tanabe mean | MATHEMATICS | spectral geometric mean | MATHEMATICS, APPLIED | sagae-tanabe mean | INEQUALITIES | positive definite operator | geometric mean | log-euclidean mean

Lie–Trotter formula | Log-Euclidean mean | Sagae–Tanabe mean | Geometric mean | Positive definite operator | Spectral geometric mean | Lie-Trotter formula | Sagae-Tanabe mean | MATHEMATICS | spectral geometric mean | MATHEMATICS, APPLIED | sagae-tanabe mean | INEQUALITIES | positive definite operator | geometric mean | log-euclidean mean

Journal Article

Journal of Modern Optics, ISSN 0950-0340, 07/2015, Volume 62, Issue 13, pp. 1081 - 1090

In this paper, we investigate a thermal coherent state defined with the Lie-Trotter product formula under the formalism of the thermo field dynamics...

thermo field dynamics | thermal coherent state | optical parametric oscillator laser | Lie-Trotter product formula | quantum optics | SYSTEM | OPTICAL PARAMETRIC OSCILLATOR | SQUEEZED STATES | ATOMIC FLUORESCENCE SPECTROMETRY | OPTICS | OPERATORS | Physics - Quantum Physics

thermo field dynamics | thermal coherent state | optical parametric oscillator laser | Lie-Trotter product formula | quantum optics | SYSTEM | OPTICAL PARAMETRIC OSCILLATOR | SQUEEZED STATES | ATOMIC FLUORESCENCE SPECTROMETRY | OPTICS | OPERATORS | Physics - Quantum Physics

Journal Article

Semigroup Forum, ISSN 0037-1912, 6/2012, Volume 84, Issue 3, pp. 499 - 504

...–Trotter product formula.

Linear semigroups of operators, counterexample | Mathematics | Algebra | Lie–Trotter product | Lie-Trotter product | MATHEMATICS

Linear semigroups of operators, counterexample | Mathematics | Algebra | Lie–Trotter product | Lie-Trotter product | MATHEMATICS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2017, Volume 453, Issue 1, pp. 195 - 211

...–Trotter formula and related unitarily invariant norm inequalities for the Cartan barycenter as the main application of log-majorization.

Lie–Trotter formula | Wasserstein distance | Log-majorization | Unitarily invariant norm | Cartan barycenter | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Trotter formula | INEQUALITIES | MATRICES

Lie–Trotter formula | Wasserstein distance | Log-majorization | Unitarily invariant norm | Cartan barycenter | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Trotter formula | INEQUALITIES | MATRICES

Journal Article

Acta mathematica scientia, ISSN 0252-9602, 05/2020, Volume 40, Issue 3, pp. 659 - 669

Suppose that A and B are two positive-definite matrices, then, the limit of (A(p/2)B(p)A(p/2))(1/p) as p tends to 0 can be obtained by the well known Lie-Trotter formula...

MATHEMATICS | Lie-Trotter formula | positive-definite matrix | Hadamard product | reciprocal Lie-Trotter formula

MATHEMATICS | Lie-Trotter formula | positive-definite matrix | Hadamard product | reciprocal Lie-Trotter formula

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 06/2016, Volume 64, Issue 6, pp. 1220 - 1235

Let and be positive semidefinite matrices. The limit of the expression as tends to is given by the well-known Lie-Trotter formula...

Lie-Trotter formula | Grassmannian manifold | Primary: 15A42 | reciprocal Lie-Trotter formula | log-majorization | antisymmetric tensor power | positive semidefinite matrix | operator mean | geometric mean | Lie–Trotter formula | reciprocal Lie–Trotter formula | INEQUALITY | 15A16 | 47A64 | MATHEMATICS | Algebra | Matrices (mathematics) | Mathematical analysis | Matrix methods | Formulas (mathematics) | Images

Lie-Trotter formula | Grassmannian manifold | Primary: 15A42 | reciprocal Lie-Trotter formula | log-majorization | antisymmetric tensor power | positive semidefinite matrix | operator mean | geometric mean | Lie–Trotter formula | reciprocal Lie–Trotter formula | INEQUALITY | 15A16 | 47A64 | MATHEMATICS | Algebra | Matrices (mathematics) | Mathematical analysis | Matrix methods | Formulas (mathematics) | Images

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 2/2018, Volume 170, Issue 4, pp. 684 - 699

...–Suzuki formula enable us to extend Chatterjee’s proof for the random field Ising model to the quantum model.

Interpolation | The Ghirlanda–Guerra identities | The Lie–Trotter–Suzuki formula | Physical Chemistry | Theoretical, Mathematical and Computational Physics | The FKG inequality | Transverse field Ising model | Quantum Physics | Quantum spin systems | Gaussian random field | Physics | Statistical Physics and Dynamical Systems | The Lie-Trotter-Suzuki formula | SPIN SYSTEMS | The Ghirlanda-Guerra identities | STATE | PHYSICS, MATHEMATICAL

Interpolation | The Ghirlanda–Guerra identities | The Lie–Trotter–Suzuki formula | Physical Chemistry | Theoretical, Mathematical and Computational Physics | The FKG inequality | Transverse field Ising model | Quantum Physics | Quantum spin systems | Gaussian random field | Physics | Statistical Physics and Dynamical Systems | The Lie-Trotter-Suzuki formula | SPIN SYSTEMS | The Ghirlanda-Guerra identities | STATE | PHYSICS, MATHEMATICAL

Journal Article

Semigroup Forum, ISSN 0037-1912, 10/2017, Volume 95, Issue 2, pp. 345 - 365

We investigate Lie–Trotter product formulae for abstract nonlinear evolution equations with delay...

Order of convergence | Algebra | C_0$$ C 0 -semigroups | Operator splitting | Mathematics | Lie–Trotter product formula | Delay equation | semigroups | MATHEMATICS | NONLINEAR SEMIGROUPS | C-0-semigroups | Lie-Trotter product formula | Analysis | Numerical analysis

Order of convergence | Algebra | C_0$$ C 0 -semigroups | Operator splitting | Mathematics | Lie–Trotter product formula | Delay equation | semigroups | MATHEMATICS | NONLINEAR SEMIGROUPS | C-0-semigroups | Lie-Trotter product formula | Analysis | Numerical analysis

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2005, Volume 396, Issue 1-3, pp. 353 - 372

...–Trotter formulae, which extend the original Lie–Trotter formula, and the α-mean variant of the original Lie...

Log majorization | Logarithmic trace inequality | Generalized Lie–Trotter formula | Generalized Lie-Trotter formula | MATHEMATICS | MATHEMATICS, APPLIED | MEAN THEORETIC APPROACH | logarithmic trace inequality | GRAND FURUTA INEQUALITY | log majorization | SIMPLIFIED PROOF | generalized Lie-Trotter formula | ENTROPY

Log majorization | Logarithmic trace inequality | Generalized Lie–Trotter formula | Generalized Lie-Trotter formula | MATHEMATICS | MATHEMATICS, APPLIED | MEAN THEORETIC APPROACH | logarithmic trace inequality | GRAND FURUTA INEQUALITY | log majorization | SIMPLIFIED PROOF | generalized Lie-Trotter formula | ENTROPY

Journal Article

11.
Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians

International Journal of Quantum Information, ISSN 0219-7499, 03/2017, Volume 15, Issue 2

... on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian...

digital representation | Lie-Trotter formula | Baker-Campbell-Hausdorff expansion | Grover's algorithm | Chebyshev polynomials | Hamiltonian evolution | projection and reflection operators | ALGORITHMS | FORMULA | PHYSICS, MATHEMATICAL | Baker-Campbell-Hausdoff expansion | COMPUTER SCIENCE, THEORY & METHODS | SIMULATING SPARSE HAMILTONIANS | DEPENDENT SCHRODINGER-EQUATION | PHYSICS, PARTICLES & FIELDS

digital representation | Lie-Trotter formula | Baker-Campbell-Hausdorff expansion | Grover's algorithm | Chebyshev polynomials | Hamiltonian evolution | projection and reflection operators | ALGORITHMS | FORMULA | PHYSICS, MATHEMATICAL | Baker-Campbell-Hausdoff expansion | COMPUTER SCIENCE, THEORY & METHODS | SIMULATING SPARSE HAMILTONIANS | DEPENDENT SCHRODINGER-EQUATION | PHYSICS, PARTICLES & FIELDS

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 12/2016, Volume 59, Issue 4, pp. 673 - 681

Let $X\left( n \right)$ , for $n\,\in \,\mathbb{N}$ , be the set of all subsets of a metric space $\left( x,\,d \right)$ of cardinality at most $n$ . The set...

Lie-Trotter-Kato formula | Gradient flow | Hadamard space | Finite subset space | Lipschitz retraction | MATHEMATICS | FINITE SUBSETS | METRIC-SPACES | MAPS | finite subset space | EMBEDDINGS | gradient flow

Lie-Trotter-Kato formula | Gradient flow | Hadamard space | Finite subset space | Lipschitz retraction | MATHEMATICS | FINITE SUBSETS | METRIC-SPACES | MAPS | finite subset space | EMBEDDINGS | gradient flow

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2017, Volume 533, pp. 118 - 131

.... As a consequence we have a version of Lie–Trotter formula and a related unitarily invariant norm inequality...

Lie–Trotter formula | Wasserstein distance | Cartan barycenter | Riemannian trace metric | Probability measure | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Trotter formula | INEQUALITIES

Lie–Trotter formula | Wasserstein distance | Cartan barycenter | Riemannian trace metric | Probability measure | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Trotter formula | INEQUALITIES

Journal Article

Computer Physics Communications, ISSN 0010-4655, 12/2014, Volume 185, Issue 12, pp. 3094 - 3098

...–Suzuki product formula, are presented for solving the time-dependent Maxwell equations in double-dispersive electromagnetic materials...

Split-step finite difference time domain (SS-FDTD) | Lie–Trotter–Suzuki product formula | Double-dispersive electromagnetic material | Alternating direction implicit (ADI) | Locally one dimension (LOD) | Lie-Trotter-Suzuki product formula | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Lie Trotter Suzuki product formula | PHYSICS, MATHEMATICAL | MAXWELLS EQUATIONS | STATISTICAL PHYSICS | Electromagnetism | Algorithms | Accuracy | Mathematical analysis | Finite difference time domain method | Time domain | Mathematical models | Dispersions | Computational efficiency | Three dimensional

Split-step finite difference time domain (SS-FDTD) | Lie–Trotter–Suzuki product formula | Double-dispersive electromagnetic material | Alternating direction implicit (ADI) | Locally one dimension (LOD) | Lie-Trotter-Suzuki product formula | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Lie Trotter Suzuki product formula | PHYSICS, MATHEMATICAL | MAXWELLS EQUATIONS | STATISTICAL PHYSICS | Electromagnetism | Algorithms | Accuracy | Mathematical analysis | Finite difference time domain method | Time domain | Mathematical models | Dispersions | Computational efficiency | Three dimensional

Journal Article

15.
Full Text
Trotter–Kato theorems for bi-continuous semigroups and applications to Feller semigroups

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2004, Volume 289, Issue 2, pp. 477 - 492

.... As a consequence, we obtain a Lie–Trotter product formula and apply it to Feller semigroups generated by second order elliptic differential operators with unbounded...

Elliptic second order differential operators with unbounded coefficients | Lie–Trotter product formula | Bi-continuous semigroups | Lie-Trotter product formula | MATHEMATICS | MATHEMATICS, APPLIED | bi-continuous semigroups | elliptic second order differential operators with unbounded coefficients

Elliptic second order differential operators with unbounded coefficients | Lie–Trotter product formula | Bi-continuous semigroups | Lie-Trotter product formula | MATHEMATICS | MATHEMATICS, APPLIED | bi-continuous semigroups | elliptic second order differential operators with unbounded coefficients

Journal Article

Operators and Matrices, ISSN 1846-3886, 12/2017, Volume 11, Issue 4, pp. 1047 - 1056

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2014, Volume 460, pp. 1 - 16

The semigroup of Hamiltonians acting on the cone of positive definite matrices via linear fractional transformations satisfies the Birkhoff contraction formula for the Thompson metric...

Lie–Trotter formula | Positive linear map | Lyapunov and Stein operator | Hamiltonian | Thompson metric | Positive definite matrix | Lie-Trotter formula | MATHEMATICS | MATHEMATICS, APPLIED | FORMULA

Lie–Trotter formula | Positive linear map | Lyapunov and Stein operator | Hamiltonian | Thompson metric | Positive definite matrix | Lie-Trotter formula | MATHEMATICS | MATHEMATICS, APPLIED | FORMULA

Journal Article

Sbornik: Mathematics, ISSN 1064-5616, 10/2009, Volume 200, Issue 10, pp. 1495 - 1519

This paper is concerned with the abstract Cauchy problem x = Ax, x(0) = x(0) is an element of D(A), where A is a densely defined linear operator on a Banach...

Lie-Trotter theorem | Semigroup | Chernoffs theorem | MATHEMATICS | semigroup | Chernoff's theorem | FORMULA

Lie-Trotter theorem | Semigroup | Chernoffs theorem | MATHEMATICS | semigroup | Chernoff's theorem | FORMULA

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2012, Volume 1493, pp. 994 - 997

Conference Proceeding

OPERATORS AND MATRICES, ISSN 1846-3886, 12/2017, Volume 11, Issue 4, pp. 1047 - 1056

The main purpose of this paper is to present satisfactory versions of the Chernoff product formula and of the Lie-Trotter product formula for C-0 - semigroups on the dual of a Banach space...

MATHEMATICS | C-0-semigroup | approximation | L-INFINITY | Chernoff product formula | Lie-Trotter product formula | UNIQUENESS

MATHEMATICS | C-0-semigroup | approximation | L-INFINITY | Chernoff product formula | Lie-Trotter product formula | UNIQUENESS

Journal Article

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