Mathematische Zeitschrift, ISSN 0025-5874, 12/2017, Volume 287, Issue 3, pp. 967 - 984

Using estimates of the law of the iterated logarithm type, a sharp sufficient condition for a compact set to be removable for analytic functions in the little...

30B40 | Mathematics, general | Mathematics | MATHEMATICS | APPROXIMATION | BMO | SETS

30B40 | Mathematics, general | Mathematics | MATHEMATICS | APPROXIMATION | BMO | SETS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 10/2019, Volume 91, Issue 5, pp. 1 - 15

Based on our paper (Dan et al. in J Funct Anal 273:559–597, 2017), we continue the study on totally Abelian analytic Toeplitz operators on the Hardy space....

The totally Abelian property | Finite Blaschke products | Secondary 30B40 | Analysis | Mathematics | Distinguished varieties | Primary 47C15

The totally Abelian property | Finite Blaschke products | Secondary 30B40 | Analysis | Mathematics | Distinguished varieties | Primary 47C15

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 03/2018, Volume 43, Issue 3, pp. 448 - 466

We prove local unique continuation across the boundary and boundary uniqueness results for solutions of the Helmholtz equation in a neighborhood of the origin...

Helmholtz's equations | 30B40 | unique continuation | Primary: 35J05 | Hopf lemma | Secondary: 31B25 | 35B60 | Helmholtz’s equations | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY | HOLOMORPHIC MAPPINGS | Helmholtz equations

Helmholtz's equations | 30B40 | unique continuation | Primary: 35J05 | Hopf lemma | Secondary: 31B25 | 35B60 | Helmholtz’s equations | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY | HOLOMORPHIC MAPPINGS | Helmholtz equations

Journal Article

Analysis, ISSN 0174-4747, 08/2016, Volume 36, Issue 3, pp. 205 - 210

Many Dirichlet series are either continuable to the whole complex plane or admit half-planes as their maximal domain of meromorphic continuation. Here we prove...

Riemann zeta function | Dirichlet series | 11M41 | 30B40 | meromorphic continuation

Riemann zeta function | Dirichlet series | 11M41 | 30B40 | meromorphic continuation

Journal Article

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, 9/2017, Volume 72, Issue 5, pp. 199 - 202

The paper contains results on localization of singularities for the power series (in terms of their coefficients) on boundary arcs of the disk of convergence.

analytic continuation | 30B10 | 30B40 | Mathematics, general | Mathematics | singularities of power series | Power series

analytic continuation | 30B10 | 30B40 | Mathematics, general | Mathematics | singularities of power series | Power series

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 11/2019, Volume 50, Issue 2, pp. 433 - 458

In this paper, we state some q-analogs of the famous Ramanujan Master Theorem. As an application, we compute some values of Jackson’s q-integrals that involve...

q -Mellin transform | 30D10 | 30B40 | Functions of a Complex Variable | Analytic continuation | Field Theory and Polynomials | Mathematics | 33D15 | Ramanujan Master Theorem | Fourier Analysis | 33D60 | Number Theory | Combinatorics | q-Mellin transform

q -Mellin transform | 30D10 | 30B40 | Functions of a Complex Variable | Analytic continuation | Field Theory and Polynomials | Mathematics | 33D15 | Ramanujan Master Theorem | Fourier Analysis | 33D60 | Number Theory | Combinatorics | q-Mellin transform

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 6/2017, Volume 88, Issue 2, pp. 249 - 268

Several representation theorems of multipliers are derived: in terms of analytic functionals, and germs of holomorphic functions. The co-induced topology via...

Analytic functional | 30B40 | Dilation set | Analysis | 44A35 | Hadamard multiplication | Multiplier | Spaces of holomorphic functions | Mathematics | 46F15 | 30H10 | MATHEMATICS

Analytic functional | 30B40 | Dilation set | Analysis | 44A35 | Hadamard multiplication | Multiplier | Spaces of holomorphic functions | Mathematics | 46F15 | 30H10 | MATHEMATICS

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 11/2018, Volume 12, Issue 8, pp. 1835 - 1844

The limit q-Bernstein operator $$B_q$$ Bq appears as a limit for a sequence of the q-Bernstein or for a sequence of the q-Meyer-König and Zeller operators in...

Limit q -Bernstein operator | Operator Theory | Secondary 26E10 | Primary 30B40 | Analysis | Divided difference | Mathematics, general | Mathematics | Analytic function | Limit q-Bernstein operator | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE

Limit q -Bernstein operator | Operator Theory | Secondary 26E10 | Primary 30B40 | Analysis | Divided difference | Mathematics, general | Mathematics | Analytic function | Limit q-Bernstein operator | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 1/2015, Volume 104, Issue 1, pp. 61 - 67

For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric...

Mathematics, general | Mathematics | Secondary 30F99 | Analytic arc | Primary 30B40 | Analytic continuation | MATHEMATICS

Mathematics, general | Mathematics | Secondary 30F99 | Analytic arc | Primary 30B40 | Analytic continuation | MATHEMATICS

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 01/2018, Volume 29, Issue 1, pp. 21 - 42

The Lauricella function , which is a generalized hypergeometric function of N variables, and a corresponding system of partial differential equations are...

systems of PDEs | 33C65 | 30B40 | 33C6 | analytic continuation formulas | Lauricella function | Multiple hypergeometric functions | 33C90 | Barnes-type integrals | Schwartz-Christoffel integral | Schwartz–Christoffel integral | MATHEMATICS, APPLIED | EQUATIONS | MATHEMATICS | F-D | FORMULAS | Hypergeometric functions | Partial differential equations | Formulas (mathematics) | Gauss equation

systems of PDEs | 33C65 | 30B40 | 33C6 | analytic continuation formulas | Lauricella function | Multiple hypergeometric functions | 33C90 | Barnes-type integrals | Schwartz-Christoffel integral | Schwartz–Christoffel integral | MATHEMATICS, APPLIED | EQUATIONS | MATHEMATICS | F-D | FORMULAS | Hypergeometric functions | Partial differential equations | Formulas (mathematics) | Gauss equation

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 3/2019, Volume 188, Issue 3, pp. 467 - 493

Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are...

Molecular decomposition | Fourier multipliers | 30B40 | Hardy spaces | Mathematics | Holomorphic functions | 30H25 | Besov spaces | Distributions | Triebel–Lizorkin spaces | 30H10 | Hardy–Sobolev spaces | 42A16 (primary) and 30B30 | Mathematics, general | 42A05 | 42A45 (secondary) | MATHEMATICS | Triebel-Lizorkin spaces | Hardy-Sobolev spaces | COEFFICIENT MULTIPLIERS | BERGMAN | OPERATORS

Molecular decomposition | Fourier multipliers | 30B40 | Hardy spaces | Mathematics | Holomorphic functions | 30H25 | Besov spaces | Distributions | Triebel–Lizorkin spaces | 30H10 | Hardy–Sobolev spaces | 42A16 (primary) and 30B30 | Mathematics, general | 42A05 | 42A45 (secondary) | MATHEMATICS | Triebel-Lizorkin spaces | Hardy-Sobolev spaces | COEFFICIENT MULTIPLIERS | BERGMAN | OPERATORS

Journal Article

Quaestiones Mathematicae, ISSN 1607-3606, 04/2019, Volume 42, Issue 4, pp. 465 - 478

The aim of this paper is to investigate some classes of higher-order Apostol-type numbers and Apostol-type polynomials. We construct Lerch-type zeta functions...

11S80 | 30B40 | Hurwitz-Lerch zeta function | 11S40 | 33E20 | 44A20 | polylogarithm function | Primary 11B68 | multiplication formula | Riemann and Hurwitz (or generalized) zeta functions | functional equation | Euler numbers and Euler polynomials | Lerch zeta function | Bernoulli numbers and Bernoulli polynomials | Secondary 26C05 | Mellin transformation | Q-EXTENSIONS | UNIFIED PRESENTATION | GENERATING-FUNCTIONS | BERNOULLI | SUMS | MATHEMATICS | EULER POLYNOMIALS

11S80 | 30B40 | Hurwitz-Lerch zeta function | 11S40 | 33E20 | 44A20 | polylogarithm function | Primary 11B68 | multiplication formula | Riemann and Hurwitz (or generalized) zeta functions | functional equation | Euler numbers and Euler polynomials | Lerch zeta function | Bernoulli numbers and Bernoulli polynomials | Secondary 26C05 | Mellin transformation | Q-EXTENSIONS | UNIFIED PRESENTATION | GENERATING-FUNCTIONS | BERNOULLI | SUMS | MATHEMATICS | EULER POLYNOMIALS

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 10/2015, Volume 66, Issue 5, pp. 2871 - 2879

We consider the deformation of a nanocomposite by incorporating the effect of surface elasticity on the finite plane deformations of a circular inhomogeneity...

30B40 | 34M45 | 35Q74 | Theoretical and Applied Mechanics | 74M25 | Engineering | Mathematical Methods in Physics | Harmonic material | Finite deformation | Size-dependent elastic field | Inhomogeneity | 74B20 | Surface elasticity | ELLIPSOIDAL INCLUSION | MATHEMATICS, APPLIED | SOLIDS | DEFORMATIONS | ELASTIC FIELD | STRESSES | Mechanical engineering | Analysis | Differential equations

30B40 | 34M45 | 35Q74 | Theoretical and Applied Mechanics | 74M25 | Engineering | Mathematical Methods in Physics | Harmonic material | Finite deformation | Size-dependent elastic field | Inhomogeneity | 74B20 | Surface elasticity | ELLIPSOIDAL INCLUSION | MATHEMATICS, APPLIED | SOLIDS | DEFORMATIONS | ELASTIC FIELD | STRESSES | Mechanical engineering | Analysis | Differential equations

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 05/2015, Volume 92, Issue 5, pp. 1025 - 1038

In this paper we consider the problem of analytic continuation of analytic function on a strip domain, where the data are given only on the real axis. This is...

analytic continuation | error estimate | 30B40 | 42C40 | regularization | Meyer wavelet | 65J20 | 47A52 | 65T60 | ill-posed problem | CHARACTERISTIC CAUCHY-PROBLEM | MATHEMATICS, APPLIED | SIDEWAYS HEAT-EQUATION | TRANSFORM | PARABOLIC EQUATION | Wavelet | Stability | Computer simulation | Perturbation methods | Mathematical analysis | Mathematical models | Estimates | Regularization

analytic continuation | error estimate | 30B40 | 42C40 | regularization | Meyer wavelet | 65J20 | 47A52 | 65T60 | ill-posed problem | CHARACTERISTIC CAUCHY-PROBLEM | MATHEMATICS, APPLIED | SIDEWAYS HEAT-EQUATION | TRANSFORM | PARABOLIC EQUATION | Wavelet | Stability | Computer simulation | Perturbation methods | Mathematical analysis | Mathematical models | Estimates | Regularization

Journal Article

15.
Full Text
Representations for the derivative at zero and finite parts of the Barnes zeta function

Integral Transforms and Special Functions, ISSN 1065-2469, 06/2017, Volume 28, Issue 6, pp. 423 - 442

We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case....

11M41 | 30E20 | zeta functions | 30B40 | Barnes zeta function | 33E20 | multiple zeta function | Barnes gamma function | gamma function | multiple gamma function | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | DETERMINANTS | MULTIPLE GAMMA-FUNCTION | Poles | Integrals | Mathematical analysis | Transforms | Derivatives | Representations | Logarithms | Gamma function

11M41 | 30E20 | zeta functions | 30B40 | Barnes zeta function | 33E20 | multiple zeta function | Barnes gamma function | gamma function | multiple gamma function | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | DETERMINANTS | MULTIPLE GAMMA-FUNCTION | Poles | Integrals | Mathematical analysis | Transforms | Derivatives | Representations | Logarithms | Gamma function

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2016, Volume 2016, Issue 1, pp. 1 - 14

In this paper, by using p-adic Volkenborn integral, and generating functions, we give some properties of the Bernstein basis functions, the Apostol-Daehee...

Stirling numbers of the first kind and the second kind | 26C10 | generating function | Mathematics | 30C15 | Daehee numbers and polynomials | functional equation | Mathematics, general | Bernstein basis functions | Apostol-Daehee numbers | 26C05 | derivative equation | 11S80 | 30B40 | 11S40 | 12D10 | 11B68 | Apostol-Bernoulli numbers and polynomials | Ordinary Differential Equations | Functional Analysis | Analysis | array polynomials | Difference and Functional Equations | Bernoulli numbers and polynomials | Partial Differential Equations | MATHEMATICS, APPLIED | IDENTITIES | GENERATING-FUNCTIONS | BERNOULLI | STIRLING TYPE NUMBERS | MATHEMATICS | EULER | Partial differential equations | Integrals | Integral equations | Mathematical analysis | Mathematical models | Polynomials | Representations | Combinatorial analysis

Stirling numbers of the first kind and the second kind | 26C10 | generating function | Mathematics | 30C15 | Daehee numbers and polynomials | functional equation | Mathematics, general | Bernstein basis functions | Apostol-Daehee numbers | 26C05 | derivative equation | 11S80 | 30B40 | 11S40 | 12D10 | 11B68 | Apostol-Bernoulli numbers and polynomials | Ordinary Differential Equations | Functional Analysis | Analysis | array polynomials | Difference and Functional Equations | Bernoulli numbers and polynomials | Partial Differential Equations | MATHEMATICS, APPLIED | IDENTITIES | GENERATING-FUNCTIONS | BERNOULLI | STIRLING TYPE NUMBERS | MATHEMATICS | EULER | Partial differential equations | Integrals | Integral equations | Mathematical analysis | Mathematical models | Polynomials | Representations | Combinatorial analysis

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 2/2012, Volume 6, Issue 1, pp. 257 - 274

For two open sets Ω1, Ω2 in the extended complex plane, we define a Hadamard product as an operator from H(Ω1) × H(Ω2) to H(Ω1 * Ω2), where Ω1 * Ω2 is the...

Operator Theory | 30B40 | Analysis | Analytic continuation | Mathematics, general | Mathematics | Hadamard product | MATHEMATICS | MATHEMATICS, APPLIED

Operator Theory | 30B40 | Analysis | Analytic continuation | Mathematics, general | Mathematics | Hadamard product | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 3/2017, Volume 17, Issue 1, pp. 129 - 138

It is known that unimodular eigenvalues of an operator can give information about its dynamical behaviour. Recently, some situations have been characterized in...

Functions of exponential type | Computational Mathematics and Numerical Analysis | 30B40 | Functions of a Complex Variable | Analysis | 37B99 | Frequently hypercyclic operators | Growth of entire functions | Mathematics | 30D15 | MATHEMATICS | MATHEMATICS, APPLIED

Functions of exponential type | Computational Mathematics and Numerical Analysis | 30B40 | Functions of a Complex Variable | Analysis | 37B99 | Frequently hypercyclic operators | Growth of entire functions | Mathematics | 30D15 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 8/2016, Volume 67, Issue 4, pp. 1 - 17

We investigate the anti-plane shear problem of a curvilinear crack lying along the interface of an arbitrarily shaped elastic inhomogeneity embedded in an...

30B40 | Faber series | Inhomogeneity of arbitrary shape | 15A06 | 74R10 | 35Q74 | Theoretical and Applied Mechanics | 30E25 | Curvilinear interface crack | Engineering | Mathematical Methods in Physics | 35Q15 | Conformal mapping | Analytical solution | Riemann–Hilbert problem | MATHEMATICS, APPLIED | Riemann-Hilbert problem | FIELD | INCLUSION | ELLIPTIC INHOMOGENEITY | INTERFACE CRACK | Cracks | Shear | Algebra | Debonding | Analytic functions | Matrices (mathematics) | Mathematical analysis | Inhomogeneity

30B40 | Faber series | Inhomogeneity of arbitrary shape | 15A06 | 74R10 | 35Q74 | Theoretical and Applied Mechanics | 30E25 | Curvilinear interface crack | Engineering | Mathematical Methods in Physics | 35Q15 | Conformal mapping | Analytical solution | Riemann–Hilbert problem | MATHEMATICS, APPLIED | Riemann-Hilbert problem | FIELD | INCLUSION | ELLIPTIC INHOMOGENEITY | INTERFACE CRACK | Cracks | Shear | Algebra | Debonding | Analytic functions | Matrices (mathematics) | Mathematical analysis | Inhomogeneity

Journal Article

Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 2011, Volume 45, Issue 1, pp. 43 - 53

We consider the Dirichlet series associated to the number of representations of an integer as a sum of primes. Assuming certain reasonable hypotheses on the...

Meromorphic continuation | Circle method | Goldbach numbers | 11M41 | 30B40 | meromorphic continuation | 11P32 | circle method | 1P55

Meromorphic continuation | Circle method | Goldbach numbers | 11M41 | 30B40 | meromorphic continuation | 11P32 | circle method | 1P55

Journal Article

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