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Advances in Dixmier traces and applications (Q3297180)

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Language	Label	Description	Also known as
English	Advances in Dixmier traces and applications	scientific article

Statements

scholarly article

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Advances in Dixmier traces and applications (English)

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Pheodor A. Sukochev

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Advances in Noncommutative Geometry

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publication date

3 July 2020

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zbMATH Keywords

singular trace

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Dixmier trace

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noncommutative geometry

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-030-29597-4_9

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A note on the Wodzicki residue

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On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations

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Singular traces and compact operators

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Analysis, Geometry and Quantum Field Theory

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Invariant Banach limits and their extreme points

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Log majorization and complementary Golden-Thompson type inequalities

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Localized Eigenfunctions of the Laplacian on p.c.f. Self-Similar Sets

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Characterization of pseudodifferential operator and application

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Type II non-commutative geometry. I: Dixmier trace in von Neumann algebras

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ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS

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Commutators of Operators on Hilbert Space

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Two-sided ideals and congruences in the ring of bounded operators in Hilbert space

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Integration on locally compact noncommutative spaces

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The Hochschild class of the Chern character for semifinite spectral triples

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The local index formula in semifinite von Neumann algebras. I: Spectral flow

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On unbounded \(p\)-summable Fredholm modules

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Spectral flow and Dixmier traces

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The Dixmier trace and asymptotics of zeta functions

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Measurable operators and the asymptotics of heat kernels and zeta functions

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Universal measurability and the Hochschild class of the Chern character

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Dixmier traces and some applications in non-commutative geometry

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The spectral action principle

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The action functional in non-commutative geometry

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Dixmier trace, Fredholm modules and Riemannian geometry

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Geometry from the spectral point of view

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Gravity coupled with matter and the foundation of non-commutative geometry

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Conformal trace theorem for Julia sets of quadratic polynomials

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The local index formula in noncommutative geometry

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Non-commutative differential geometry

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Noncommutative geometry and reality

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A short survey of noncommutative geometry

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Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes

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Elliptic pseudo-differential operators - an abstract theory

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On pseudo-differential operators and smoothness of special Lie-group representations

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Gel'Fand Theory of Pseudo Differential Operators

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Weak type estimates for singular values and the number of bound states of Schrödinger operators

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Singular symmetric functionals

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Singular symmetric functionals and Banach limits with additional invariance properties

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Symmetric functionals and singular traces

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Commutator structure of operator ideals

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Sums of commutators in non-commutative Banach function spaces.

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Which Operators are the Self-Commutators of Compact Operators?

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Weyl's law and Connes' trace theorem for noncommutative two tori

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Noncommutative residues for pseudo-differential operators on the noncommutative two-torus

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Cwikel's theorem and the CLR inequality

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On a spectral analysis for the Sierpiński gasket.

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Moyal planes are spectral triples

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Dixmier traces on noncompact isospectral deformations

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Dixmier traces and extrapolation description of noncommutative Lorentz spaces

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The spectral geometry of a Riemannian manifold

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Smooth Fourier multipliers in group algebras via Sobolev dimension

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Algebras of distributions suitable for phase-space quantum mechanics. I

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On the principles of elementary quantum mechanics

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An algebra of pseudodifferential operators and quantum mechanics in phase space

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Functional calculus of pseudodifferential boundary problems.

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Dimensions and singular traces for spectral triples, with applications to fractals

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ON THE DOMAIN OF SINGULAR TRACES

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A new proof of Weyl's formula on the asymptotic distribution of eigenvalues

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Commutators of Operators

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Commutators of Operators, II

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Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet

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Zeta function regularization of path integrals in curved spacetime

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Traces of differential forms and Hochschild homology

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On the number of bound states for Schrödinger operators with operator-valued potentials

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100 years of Weyl's law

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An algebra of pseudo‐differential operators

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Schatten classes and commutators of singular integral operators

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Traces on operator ideals and arithmetic means

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Log-periodic asymptotic expansion of the spectral partition function for self-similar sets

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Banach limits and the Čech compactification of a countable discrete set

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Gravity, non-commutative geometry and the Wodzicki residue

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Unusual Traces on Operator Ideals

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Trace-class operators and commutators

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Spectral characterization of sums of commutators I

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Fully symmetric functionals on a Marcinkiewicz space are Dixmier traces

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Rearrangement-Invariant Functionals with Applications to Traces on Symmetrically Normed Ideals

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Symmetric norms and spaces of operators

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Traces of compact operators and the noncommutative residue

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The Dirac operator and gravitation

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The History of Stokes' Theorem

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Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals

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Noncommutative integration calculus

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The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums

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Fractal Geometry, Complex Dimensions and Zeta Functions

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Completeness of quasi-normed operator ideals generated by \(s\)-numbers

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Cwikel estimates revisited

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Brownian motion on nested fractals

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Measures from Dixmier traces and zeta functions

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Dixmier traces as singular symmetric functionals and applications to measurable operators

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Noncommutative residues and a characterisation of the noncommutative integral

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Quantum differentiability of essentially bounded functions on Euclidean space

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Singular traces. Theory and applications

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A contribution to the theory of divergent sequences

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Algebraic aspects of nonlinear differential equations

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On the generalized limit of bounded sequences

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A \(C^*\)-algebraic approach to the principal symbol. II

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Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds

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Computation of symbols on 𝐶*-algebras of singular integral operators

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Dixmier's trace for boundary value problems

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Trace functionals for a class of pseudo-differential operators in \(\mathbb R^n\)

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On commutators in ideals of compact operators

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Dixmier traces of operators on Banach and Hilbert spaces

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Operator Ideals with a Trace

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Traces and Shift Invariant Functionals

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About the Banach envelope of \(l_{1,\infty}\)

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Connes-Dixmier versus Dixmier traces

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Traces of operators and their history

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Traces on operator ideals and related linear forms on sequence ideals. I

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Traces on operator ideals and related linear forms on sequence ideals. II

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Traces on operator ideals and related linear forms on sequence ideals. III

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A new approach to operator ideals on Hilbert space and their traces

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The spectrum of shift operators and the existence of traces

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Unbounded Fredholm modules and double operator integrals

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Fréchet differentiability of the norm of \(L_p\)-spaces associated with arbitrary von Neumann algebras

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Singular traces and perturbation formulae of higher order

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Another Proof of Lidskii's Theorem on the Trace

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COMMUTATOR IDEALS AND PSEUDODIFFERENTIAL C<sup>*</sup>-ALGEBRAS

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Factorization of Summability-Preserving Generalized Limits

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On the Analytic Continuation of the Minakshisundaram-Pleijel Zeta Function for Compact Riemann Surfaces

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C*-algebras associated with irrational rotations

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Deformation quantization for actions of 𝑅^{𝑑}

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Nearly weakly orthonormal sequences, singular value estimates, and Calderon-Zygmund operators

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Pseudo-Differential Operators and Symmetries

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Some Sequence Spaces Related to the <i>l</i> <sup> <i>p</i> </sup> Spaces

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The symbols of an algebra of pseudo-differential operators

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Generalized limits and related asymptotic formulas

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Dixmier measurability in Marcinkiewicz spaces and applications

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Lidskii-type formulae for Dixmier traces

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Invariant Banach limits and applications

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Banach limits and traces on \(\mathcal{L}_{1, \infty}\)

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Analysis With Weak Trace Ideals and the Number of Bound States of Schrodinger Operators

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Existence of a meromorphic extension of spectral zeta functions on fractals

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Finite-rank approximations of spectral zeta residues

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Singular traces and residues of the $\\zeta$-function

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\(\zeta \)-function and heat kernel formulae

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Dixmier traces are weak dense in the set of all fully symmetric traces

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Which traces are spectral?

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Fubini theorem in noncommutative geometry

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Connes integration formula for the noncommutative plane

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Completeness of quasi-normed symmetric operator spaces

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Generalized limits with additional invariance properties and their applications to noncommutative geometry

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On the distinction between the classes of Dixmier and Connes-Dixmier traces

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Dixmier traces generated by exponentiation invariant generalised limits

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Beals-Cordes-type characterizations of pseudodifferential operators

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Traces on Irregular Ideals

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Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra

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The Moyal representation of quantum mechanics and special function theory

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Heat kernel expansion: user's manual

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Cwikel Type Estimates in Non‐Power Ideals

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Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation

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Local invariants of spectral asymmetry

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Identifiers

zbMATH Open document ID

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10.1007/978-3-030-29597-4_9

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3297180

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