2014, De Gruyter studies in mathematics, ISBN 9783110281231, Volume 52., xiii, 449

Book

2012, 1, Annals of mathematics studies, ISBN 9780691153551, Volume no. 179, ix, 425

This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into...

Calculus of variations | Functional analysis | Banach spaces | Mathematics | Math | Frechet spaces | Lipschitz spaces

Calculus of variations | Functional analysis | Banach spaces | Mathematics | Math | Frechet spaces | Lipschitz spaces

Book

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2019, Volume 71, Issue 1, pp. 91 - 115

Let L-1 and L-2 be nonnegative self-adjoint operators acting on L-2(X-1) and L-2 (X-2), respectively, where X-1 and X-2 are spaces of homogeneous type. Assume...

MATHEMATICS | DUALITY | BESOV-LIPSCHITZ | BMO

MATHEMATICS | DUALITY | BESOV-LIPSCHITZ | BMO

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 09/2016, Volume 261, Issue 6, pp. 3551 - 3587

We introduce a generalized index for certain meromorphic, unbounded, operator-valued functions. The class of functions is chosen such that energy parameter...

Donoghue-type M-functions | Boundary triples | Index computations for meromorphic operator-valued functions | Weyl functions | Dirichlet-to-Neumann maps | Non-self-adjoint Schrödinger operators | ELLIPTIC DIFFERENTIAL-OPERATORS | UNITARY EQUIVALENCE | BOUNDARY-VALUE-PROBLEMS | LIPSCHITZ-DOMAINS | SELF-ADJOINT EXTENSIONS | SPACE | MATHEMATICS | Non-self-adjoint Schrodinger operators | RESOLVENTS | SYMMETRIC-OPERATORS | HERGLOTZ FUNCTIONS | SPECTRA

Donoghue-type M-functions | Boundary triples | Index computations for meromorphic operator-valued functions | Weyl functions | Dirichlet-to-Neumann maps | Non-self-adjoint Schrödinger operators | ELLIPTIC DIFFERENTIAL-OPERATORS | UNITARY EQUIVALENCE | BOUNDARY-VALUE-PROBLEMS | LIPSCHITZ-DOMAINS | SELF-ADJOINT EXTENSIONS | SPACE | MATHEMATICS | Non-self-adjoint Schrodinger operators | RESOLVENTS | SYMMETRIC-OPERATORS | HERGLOTZ FUNCTIONS | SPECTRA

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 10, pp. 2779 - 2787

The goal of this paper is to unify and extend the generating functions of the generalized Bernoulli polynomials, the generalized Euler polynomials and the...

Riemann and Hurwitz (or generalized) zeta functions | Polylogarithm function | Lipschitz–Lerch zeta function | Euler numbers and Euler polynomials | Lerch zeta function | Bernoulli numbers and Bernoulli polynomials | Genocchi numbers and Genocchi polynomials | Recurrence relations | Hurwitz–Lerch zeta function | Mellin transformation | Dirichlet character | LipschitzLerch zeta function | HurwitzLerch zeta function | MATHEMATICS, APPLIED | Hurwitz-Lerch zeta function | NUMBERS | EXTENSION | Lipschitz-Lerch zeta function | ZETA | APOSTOL-BERNOULLI | FORMULAS | Genocchi numbers and Genocch polynomials | Construction | Mathematical models | Transformations | Mathematical analysis

Riemann and Hurwitz (or generalized) zeta functions | Polylogarithm function | Lipschitz–Lerch zeta function | Euler numbers and Euler polynomials | Lerch zeta function | Bernoulli numbers and Bernoulli polynomials | Genocchi numbers and Genocchi polynomials | Recurrence relations | Hurwitz–Lerch zeta function | Mellin transformation | Dirichlet character | LipschitzLerch zeta function | HurwitzLerch zeta function | MATHEMATICS, APPLIED | Hurwitz-Lerch zeta function | NUMBERS | EXTENSION | Lipschitz-Lerch zeta function | ZETA | APOSTOL-BERNOULLI | FORMULAS | Genocchi numbers and Genocch polynomials | Construction | Mathematical models | Transformations | Mathematical analysis

Journal Article

Fuzzy Sets and Systems, ISSN 0165-0114, 11/2017, Volume 326, pp. 89 - 105

We introduce and study transformations that assign to each conjunctive real-valued function F:[0,1]2→R and any pair of parameters (a,b)∈[0,1]2 a function...

Quasi-copula | Copula | Spearman's rho | Conjunctive function | Kendall's tau | Tail dependence parameters | Measure-preserving transformation | Lipschitz conjunctive function | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | DIAGONAL SECTIONS | PATCHWORK | QUASI-COPULAS | CONSTRUCTIONS | COMPUTER SCIENCE, THEORY & METHODS | BIVARIATE COPULAS

Quasi-copula | Copula | Spearman's rho | Conjunctive function | Kendall's tau | Tail dependence parameters | Measure-preserving transformation | Lipschitz conjunctive function | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | DIAGONAL SECTIONS | PATCHWORK | QUASI-COPULAS | CONSTRUCTIONS | COMPUTER SCIENCE, THEORY & METHODS | BIVARIATE COPULAS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 1, pp. 447 - 472

For a Banach function algebra A, we consider the problem of representing a continuous d-homogeneous polynomial P:A→X, where X is an arbitrary Banach space,...

Algebra of Lipschitz functions | Figà–Talamanca–Herz algebra | Orthogonally additive polynomial | Algebra of absolutely continuous functions | Algebra of differentiable functions | Fourier algebra | Figa-Talamanca-Herz algebra | MATHEMATICS, APPLIED | SPACES | DERIVATIONS | MATHEMATICS | MAPS | HOLOMORPHIC-FUNCTIONS | HYPERREFLEXIVITY | Algebra

Algebra of Lipschitz functions | Figà–Talamanca–Herz algebra | Orthogonally additive polynomial | Algebra of absolutely continuous functions | Algebra of differentiable functions | Fourier algebra | Figa-Talamanca-Herz algebra | MATHEMATICS, APPLIED | SPACES | DERIVATIONS | MATHEMATICS | MAPS | HOLOMORPHIC-FUNCTIONS | HYPERREFLEXIVITY | Algebra

Journal Article

Russian Mathematical Surveys, ISSN 0036-0279, 2016, Volume 71, Issue 4, pp. 605 - 702

The goal of this survey is a comprehensive study of operator Lipschitz functions. A continuous function f on the real line R is said to be operator Lipschitz...

Normal operators | Divided differences | Operator differentiable functions | Operator Lipschitz functions | Schur multipliers | Besov classes | Double operator integrals | Linear-fractional transformations | Carleson measures | Functions of operators | Self-adjoint operators | SMOOTH FUNCTIONS | normal operators | self-adjoint operators | double operator integrals | operator differentiable functions | divided differences | INTEGRALS | MATHEMATICS | operator Lipschitz functions | linear-fractional transformations | functions of operators | Functions (mathematics) | Operators (mathematics) | Operators | Multipliers | Planes | Integrals | Mathematical analysis | Commutators

Normal operators | Divided differences | Operator differentiable functions | Operator Lipschitz functions | Schur multipliers | Besov classes | Double operator integrals | Linear-fractional transformations | Carleson measures | Functions of operators | Self-adjoint operators | SMOOTH FUNCTIONS | normal operators | self-adjoint operators | double operator integrals | operator differentiable functions | divided differences | INTEGRALS | MATHEMATICS | operator Lipschitz functions | linear-fractional transformations | functions of operators | Functions (mathematics) | Operators (mathematics) | Operators | Multipliers | Planes | Integrals | Mathematical analysis | Commutators

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2016, Volume 171, Issue 2, pp. 481 - 503

The paper deals with positively homogeneous functions defined on a finite-dimensional space. Our attention is mainly focused on those subspaces of positively...

Difference sublinearity | Piecewise linear function | 54C35 | Mathematics | Theory of Computation | Optimization | Lipschitz continuity | Calculus of Variations and Optimal Control; Optimization | 49J52 | Positive homogeneity | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | MATHEMATICS, APPLIED | DIFFERENTIABILITY | METRICS | FAMILY | SPACE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DIFFERENCE | COEXHAUSTERS | OPTIMALITY CONDITIONS | EXHAUSTERS | Studies | Mathematical analysis | Subspaces | Paper

Difference sublinearity | Piecewise linear function | 54C35 | Mathematics | Theory of Computation | Optimization | Lipschitz continuity | Calculus of Variations and Optimal Control; Optimization | 49J52 | Positive homogeneity | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | MATHEMATICS, APPLIED | DIFFERENTIABILITY | METRICS | FAMILY | SPACE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DIFFERENCE | COEXHAUSTERS | OPTIMALITY CONDITIONS | EXHAUSTERS | Studies | Mathematical analysis | Subspaces | Paper

Journal Article

Formalized Mathematics, ISSN 1898-9934, 12/2017, Volume 25, Issue 4, pp. 269 - 281

In this article, we formalize in Mizar [1], [3] the existence and uniqueness part of the implicit function theorem. In the first section, some composition...

version: 8.1.06 5.45.1311 | identifier: NDIFF 8 | 26B10 53A07 03B35 | Banach fixed point theorem | implicit function theorem | Lipschitz continuity

version: 8.1.06 5.45.1311 | identifier: NDIFF 8 | 26B10 53A07 03B35 | Banach fixed point theorem | implicit function theorem | Lipschitz continuity

Journal Article

Formalized Mathematics, ISSN 1426-2630, 07/2019, Volume 27, Issue 2, pp. 117 - 131

In this article, we formalize differentiability of implicit function theorem in the Mizar system [3], [1]. In the first half section, properties of Lipschitz...

differentiability | 47A05 | 26B10 | 47J07 | 53A07 | implicit function | 03B35 | implicit function theorem | Lipschitz continuity | lipschitz continuity | 47a05 | 26b10 | 47j07 | 53a07 | 03b35

differentiability | 47A05 | 26B10 | 47J07 | 53A07 | implicit function | 03B35 | implicit function theorem | Lipschitz continuity | lipschitz continuity | 47a05 | 26b10 | 47j07 | 53a07 | 03b35

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 2, pp. 1287 - 1298

Under the right conditions on a compact metric space X and on a Banach space E, we give a description of the 2-local (standard) isometries on the Banach space...

Lipschitz function | Isometry | 2-iso-reflexive | 2-local isometry | VON-NEUMANN-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-2-LOCAL DERIVATIONS | THEOREM | B(H) | AUTOMORPHISMS

Lipschitz function | Isometry | 2-iso-reflexive | 2-local isometry | VON-NEUMANN-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-2-LOCAL DERIVATIONS | THEOREM | B(H) | AUTOMORPHISMS

Journal Article

13.
Full Text
Homomorphisms between algebras of Lipschitz functions with the values in function algebras

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2016, Volume 444, Issue 1, pp. 210 - 229

We give a characterization of algebra homomorphisms and isomorphisms between Banach algebras of Lipschitz functions with the values in unital commutative...

Unital commutative [formula omitted]-algebras | Algebra homomorphisms | Banach algebras of Lipschitz functions | Algebra isomorphisms | algebras | Unital commutative C | MATHEMATICS | MATHEMATICS, APPLIED | REFLEXIVITY | Unital commutative C-algebras | Algebra

Unital commutative [formula omitted]-algebras | Algebra homomorphisms | Banach algebras of Lipschitz functions | Algebra isomorphisms | algebras | Unital commutative C | MATHEMATICS | MATHEMATICS, APPLIED | REFLEXIVITY | Unital commutative C-algebras | Algebra

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 08/2018, Volume 291, Issue 11-12, pp. 1899 - 1907

In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of and in a...

46E40; Secondary: 46E15 | algebra isomorphism | Banach–Stone theorem | Primary: 46B04 | multipliers | Lipschitz maps | isometry | MATHEMATICS | METRIC-SPACES | BANACH-STONE-THEOREM | Banach-Stone theorem

46E40; Secondary: 46E15 | algebra isomorphism | Banach–Stone theorem | Primary: 46B04 | multipliers | Lipschitz maps | isometry | MATHEMATICS | METRIC-SPACES | BANACH-STONE-THEOREM | Banach-Stone theorem

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 10/2019, Volume 277, Issue 8, pp. 2697 - 2727

We develop tools for proving isomorphisms of normed spaces of Lipschitz functions over various doubling metric spaces and Banach spaces. In particular, we show...

Lipschitz functions | Lipschitz-free spaces | Orlicz spaces | Carnot groups | MATHEMATICS | SEPARATED NETS | THEOREM | PROPERTY | METRICS | GROWTH | Analysis | Numerical analysis

Lipschitz functions | Lipschitz-free spaces | Orlicz spaces | Carnot groups | MATHEMATICS | SEPARATED NETS | THEOREM | PROPERTY | METRICS | GROWTH | Analysis | Numerical analysis

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2014, Volume 266, Issue 7, pp. 4314 - 4421

We prove that given any k∈N, for each open set Ω⊆Rn and any closed subset D of Ω¯ such that Ω is locally an (ε,δ)-domain near ∂Ω∖D, there exists a linear and...

Bessel potential space and capacity | Synthesis | Locally [formula omitted]-domain | Mixed boundary value problem | Higher-order elliptic system | Ahlfors regular set | Linear extension operator | Besov and Triebel–Lizorkin spaces | Higher-order Sobolev space | Higher-order boundary trace operator | Real and complex interpolation | Locally (ε, δ)-domain | Besov and Triebel-Lizorkin spaces | DIFFERENTIABLE FUNCTIONS | Locally (epsilon, delta)-domain | STOKES SYSTEM | BESOV-SPACES | LIPSCHITZ-DOMAINS | EXTENSION-THEOREMS | INTERPOLATION | MATHEMATICS | DECOMPOSITIONS | REGULARITY | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS

Bessel potential space and capacity | Synthesis | Locally [formula omitted]-domain | Mixed boundary value problem | Higher-order elliptic system | Ahlfors regular set | Linear extension operator | Besov and Triebel–Lizorkin spaces | Higher-order Sobolev space | Higher-order boundary trace operator | Real and complex interpolation | Locally (ε, δ)-domain | Besov and Triebel-Lizorkin spaces | DIFFERENTIABLE FUNCTIONS | Locally (epsilon, delta)-domain | STOKES SYSTEM | BESOV-SPACES | LIPSCHITZ-DOMAINS | EXTENSION-THEOREMS | INTERPOLATION | MATHEMATICS | DECOMPOSITIONS | REGULARITY | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2015, Volume 21, Issue 1-3, pp. 99 - 111

•Differentiable black-box global optimization problems are considered.•A new deterministic ‘Divide-the-Best’ algorithm is proposed in its basic version.•The...

Lipschitz gradients | Deterministic methods | Global optimization | Unknown Lipschitz constant | MATHEMATICS, APPLIED | WORKING | SET | SEARCH | PHYSICS, FLUIDS & PLASMAS | INFORMATION | PHYSICS, MATHEMATICAL | SOFTWARE | STRATEGIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | LIPSCHITZ-CONSTANTS | 1ST DERIVATIVES | MINIMIZATION ALGORITHM | PARTITION | Lipschitz condition | Algorithms | Mathematical analysis | Constants | Mathematical models | Representations | Optimization | Convergence

Lipschitz gradients | Deterministic methods | Global optimization | Unknown Lipschitz constant | MATHEMATICS, APPLIED | WORKING | SET | SEARCH | PHYSICS, FLUIDS & PLASMAS | INFORMATION | PHYSICS, MATHEMATICAL | SOFTWARE | STRATEGIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | LIPSCHITZ-CONSTANTS | 1ST DERIVATIVES | MINIMIZATION ALGORITHM | PARTITION | Lipschitz condition | Algorithms | Mathematical analysis | Constants | Mathematical models | Representations | Optimization | Convergence

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 08/2014, Volume 67, Issue 8, pp. 1219 - 1262

For a family of second‐order elliptic operators with rapidly oscillating periodic coefficients, we study the asymptotic behavior of the Green and Neumann...

MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | DIRICHLET PROBLEM | LIPSCHITZ-DOMAINS | DIVERGENCE FORM | EQUATION | SINGULAR-INTEGRALS | COMPACTNESS METHODS

MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | DIRICHLET PROBLEM | LIPSCHITZ-DOMAINS | DIVERGENCE FORM | EQUATION | SINGULAR-INTEGRALS | COMPACTNESS METHODS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2010, Volume 224, Issue 3, pp. 910 - 966

It is well known that a Lipschitz function on the real line does not have to be operator Lipschitz. We show that the situation changes dramatically if we pass...

Operator Hölder functions | Multiple operator integrals | Contractions | Hölder classes | Zygmund class | Unitary operators | Operator Lipschitz function | Self-adjoint operators | Holder classes | INTEGRALS | MATHEMATICS | Operator Holder functions | LIPSCHITZ

Operator Hölder functions | Multiple operator integrals | Contractions | Hölder classes | Zygmund class | Unitary operators | Operator Lipschitz function | Self-adjoint operators | Holder classes | INTEGRALS | MATHEMATICS | Operator Holder functions | LIPSCHITZ

Journal Article

Optimization Letters, ISSN 1862-4472, 12/2018, Volume 12, Issue 8, pp. 1971 - 1980

We say that a positively homogeneous function admits a saddle representation by linear functions iff it admits both an inf-sup-representation and a...

Difference sublinear functions | Positively homogeneous functions | Saddle representation | Lipschitz continuity | Piecewise linear functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Difference sublinear functions | Positively homogeneous functions | Saddle representation | Lipschitz continuity | Piecewise linear functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Journal Article