Search results for "Mathematica"
showing 10 items of 7971 documents
Inner functions and local shape of orthonormal wavelets
2011
Abstract Conditions characterizing all orthonormal wavelets of L 2 ( R ) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet.
A new full descriptive characterization of Denjoy-Perron integral
1995
It is proved that the absolute continuity of the variational measure generated by an additive interval function \(F\) implies the differentiability almost everywhere of the function \(F\) and gives a full descriptive characterization of the Denjoy-Perron integral.
Radon–Nikodým Theorems for Finitely Additive Multimeasures
2015
In this paper we deal with interval multimeasures. We show some Radon–Nikodým theorems for such multimeasures using multivalued Henstock or Henstock–Kurzweil–Pettis derivatives. We do not use the separability assumption in the results.
Some remarks concerning Nambu mechanics
1996
The structure of Nambu-Poisson brackets is studied and we establish that any Nambu tensor is decomposable. We show that every Nambu-Poisson manifold admits a local foliation by canonical Nambu-Poisson manifolds. Finally, a cohomology for Nambu (Lie) algebras which is adapted to the study of formal deformations of Nambu structures is introduced.
An invariant analytic orthonormalization procedure with an application to coherent states
2007
We discuss a general strategy which produces an orthonormal set of vectors, stable under the action of a given set of unitary operators Aj, j=1,2,n, starting from a fixed normalized vector in H and from a set of unitary operators. We discuss several examples of this procedure and, in particular, we show how a set of coherentlike vectors can be produced and in which condition over the lattice spacing this can be done. © 2007 American Institute of Physics.
Generalized Bogoliubov transformations versus D-pseudo-bosons
2015
We demonstrate that not all generalized Bogoliubov transformations lead to D -pseudo-bosons and prove that a correspondence between the two can only be achieved with the imposition of specific constraints on the parameters defining the transformation. For certain values of the parameters, we find that the norms of the vectors in sets of eigenvectors of two related apparently non-selfadjoint number-like operators possess different types of asymptotic behavior. We use this result to deduce further that they constitute bases for a Hilbert space, albeit neither of them can form a Riesz base. When the constraints are relaxed, they cease to be Hilbert space bases but remain D -quasibases.
An Introduction to Hodge Structures
2015
We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This will lead us to the more general definition of a variation of Hodge structure and the Gauss-Manin connection. We then review the basics about mixed Hodge structures with a view towards degenerations of Hodge structures; including the canonical extension of a vector bundle with connection, Schmid’s limiting mixed Hodge structure and Steenbrink’s work in the geometric setting. Fin…
Multiplizit�ten ?unendlich-ferner? Spitzen
1979
LetX be the quotient of a bounded symmetric domainD by an arithmetically defined subgroup Γ of all analytic automorphisms ofD and letX * be theSatake-compactification ofX. In the present note, the multiplicities of the local rings of the zero-dimensional boundary components ofX * will be computed in a completely elementary manner using reduction-theory in selfadjoint homogeneous cones.
The deformation multiplicity of a map germ with respect to a Boardman symbol
2001
We define the deformation multiplicity of a map germ f: (Cn, 0) → (Cp, 0) with respect to a Boardman symbol i of codimension less than or equal to n and establish a geometrical interpretation of this number in terms of the set of Σi points that appear in a generic deformation of f. Moreover, this number is equal to the algebraic multiplicity of f with respect to i when the corresponding associated ring is Cohen-Macaulay. Finally, we study how algebraic multiplicity behaves with weighted homogeneous map germs.
Image Milnor number and 𝒜 e -codimension for maps between weighted homogeneous irreducible curves
2019
Abstract Let (X, 0) ⊂ (ℂ n , 0) be an irreducible weighted homogeneous singularity curve and let f : (X, 0) → (ℂ2, 0) be a finite map germ, one-to-one and weighted homogeneous with the same weights of (X, 0). We show that 𝒜 e -codim(X, f) = μI (f), where the 𝒜 e -codimension 𝒜 e -codim(X, f) is the minimum number of parameters in a versal deformation and μI (f) is the image Milnor number, i.e. the number of vanishing cycles in the image of a stabilization of f.