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MOBIUS-INVARIANT HILBERT SPACES IN POLYDISCS

by H. Turgay Kaptanoolu
"... We define the Dirichlet space 31 on the unit polydisc U " of C ". 2 is a semi-Hilbert space of of holomorphic functions, contains the holomorphic polynomials densely, is invariant under compositions with the biholomorphic automorphisms of U " , and its semi-norm is preserved under suc ..."
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such compositions. We show that 2 is unique with these properties. We also prove 3ί is unique if we assume that the semi-norm of a function in 3f composed with an automorphism is only equivalent in the metric sense to the semi-norm of the original function. Members of a subclass of 3f given by a norm can be writ

New action for the Hilbert-Einstein equations

by L. D. Faddeev , 906
"... Einstein’s Theory of Gravitation is the most ingenious achievement in the Theoretical Physics. It has dramatic history, experimental confirmations and beautiful geometric formulation. Its hamiltonian formulation (see e. g. [1] and refs. to fundamental papers of Dirac, ADM and others) allows for the ..."
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possibility to modify the mathematical formulation of the theory retaining the main Hilbert-Einstein equations. I begin with the parametrization of the 4-dimensional space-time M 4 by imbedding into 10-dimensional Euclidian space R 10 f A = f A (x µ), where f A, A = 1,...10 and x µ, µ = 1, 2, 3, 4

L p-boundedness of the Hilbert transform

by Kunal Narayan Chaudhury , 909
"... The Hilbert transform is essentially the only singular operator in dimension 1. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on several theoretical and physical problems across a wide range of discipli ..."
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of the Hilbert transform, namely that it is is weakly bounded on L 1 (R), and strongly bounded on L p (R) for 1 < p < ∞, and provide a self-contained derivation of the same using real-variable techniques. This note is partly based on the expositions on the Hilbert transform in [1, 3]. Context The Hilbert

MORITA EQUIVALENCE IN THE CONTEXT OF HILBERT MODULES

by unknown authors
"... Abstract. The Morita equivalence of m-regular involutive quantales in the context of the theory of Hilbert A-modules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative m-regular involutive quantales are Morita equivalent if and only if t ..."
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, such as [1] or [3]. The paper is organized as follows. First, we recall the notion of a right Hilbert A-module and related notions. In Section 1 the necessary basic properties of right Hilbert modules are established. Moreover, a categorical characterization of surjective module maps in the category of m

MORITA EQUIVALENCE IN THE CONTEXT OF HILBERT MODULES

by unknown authors
"... Abstract. The Morita equivalence of m-regular involutive quantales in the context of the theory of Hilbert A-modules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative m-regular involutive quantales are Morita equivalent if and only if t ..."
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, such as [1] or [3]. The paper is organized as follows. First, we recall the notion of a right Hilbert A-module and related notions. In Section 1 the necessary basic properties of right Hilbert modules are established. Moreover, a categorical

Local Indecomposability of Hilbert Modular Galois Representations

by Bin Zhao
"... Abstract. We prove the indecomposability of the Galois representation restricted to the p-decomposition group attached to a non CM nearly p-ordinary weight two Hilbert modular form over a totally real field F under the assumption that either the degree of F over Q is odd or the automorphic represent ..."
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representation attached to the Hilbert modular form is square integrable at some finite place of F. Contents 1. Abelian Varieties of GL(2)-type 3 2. Abelian varieties with real multiplication 6 3. Hilbert modular Shimura variety 8 4. Eigen coordinates 12

Hilbert modular forms and the Gross–Stark conjecture

by Samit Dasgupta, Henri Darmon, Robert Pollack , 2009
"... Let F be a totally real field and χ an abelian totally odd character of F. In 1988, Gross stated a p-adic analogue of Stark’s conjecture that relates the value of the derivative of the p-adic L-function associated to χ and the p-adic logarithm of a p-unit in the extension of F cut out by χ. In this ..."
Abstract - Cited by 13 (3 self) - Add to MetaCart
Let F be a totally real field and χ an abelian totally odd character of F. In 1988, Gross stated a p-adic analogue of Stark’s conjecture that relates the value of the derivative of the p-adic L-function associated to χ and the p-adic logarithm of a p-unit in the extension of F cut out by χ

Weights of Galois representations associated to Hilbert modular forms

by Michael M. Schein , 2006
"... Abstract. Let F be a totally real field, p ≥ 3 a rational prime unramified in F, and p a place of F over p. Let ρ: Gal(F/F) → GL2(Fp) be a two-dimensional mod p Galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible. ..."
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Abstract. Let F be a totally real field, p ≥ 3 a rational prime unramified in F, and p a place of F over p. Let ρ: Gal(F/F) → GL2(Fp) be a two-dimensional mod p Galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible

A Hilbert space of Dirichlet series and systems of dilated functions

by Peter Lindqvist, Kristian Seip - in L2 (0,1 , 1997
"... Abstract. For a function ϕ in L 2 (0, 1), extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates ϕ(nx), n = 1, 2, 3,..., constitutes a Riesz basis or a complete sequence in L 2 (0, 1). The problem translates into a question concerning multiplie ..."
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multipliers and cyclic vectors in the Hilbert space H of Dirichlet series f(s) = ∑ n ann −s, where the coefficients an are square summable. It proves useful to model H as the H 2 space of the infinite-dimensional polydisk, or, which is the same, the H 2 space of the character space, where a character is a

A SEMILINEAR PERTURBATION OF THE IDENTITY IN HILBERT SPACES

by Dinu Teodorescu
"... In this note we establish an existence and uniqueness result for the equation u − Au + F (u) = f where A is linear, quasi-positive and the nonlinear function F is a Lipschitz monotone operator. Let H be a real Hilbert space endowed with the inner product 〈·, · 〉 and the norm ‖· ‖ and f ∈ H. We cons ..."
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In this note we establish an existence and uniqueness result for the equation u − Au + F (u) = f where A is linear, quasi-positive and the nonlinear function F is a Lipschitz monotone operator. Let H be a real Hilbert space endowed with the inner product 〈·, · 〉 and the norm ‖· ‖ and f ∈ H. We
Results 11 - 20 of 372