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372
MOBIUSINVARIANT HILBERT SPACES IN POLYDISCS
"... We define the Dirichlet space 31 on the unit polydisc U " of C ". 2 is a semiHilbert space of of holomorphic functions, contains the holomorphic polynomials densely, is invariant under compositions with the biholomorphic automorphisms of U " , and its seminorm 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 seminorm of a function in 3f composed with an automorphism is only equivalent in the metric sense to the seminorm of the original function. Members of a subclass of 3f given by a norm can be writ
New action for the HilbertEinstein equations
, 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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Cited by 3 (1 self)
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possibility to modify the mathematical formulation of the theory retaining the main HilbertEinstein equations. I begin with the parametrization of the 4dimensional spacetime M 4 by imbedding into 10dimensional 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 pboundedness of the Hilbert transform
, 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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Cited by 1 (1 self)
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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 selfcontained derivation of the same using realvariable 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
"... Abstract. The Morita equivalence of mregular involutive quantales in the context of the theory of Hilbert Amodules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative mregular 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 Amodule 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
"... Abstract. The Morita equivalence of mregular involutive quantales in the context of the theory of Hilbert Amodules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative mregular 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 Amodule 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
"... Abstract. We prove the indecomposability of the Galois representation restricted to the pdecomposition group attached to a non CM nearly pordinary 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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Cited by 8 (1 self)
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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
, 2009
"... Let F be a totally real field and χ an abelian totally odd character of F. In 1988, Gross stated a padic analogue of Stark’s conjecture that relates the value of the derivative of the padic Lfunction associated to χ and the padic logarithm of a punit in the extension of F cut out by χ. In this ..."
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Cited by 13 (3 self)
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Let F be a totally real field and χ an abelian totally odd character of F. In 1988, Gross stated a padic analogue of Stark’s conjecture that relates the value of the derivative of the padic Lfunction associated to χ and the padic logarithm of a punit in the extension of F cut out by χ
Weights of Galois representations associated to Hilbert modular forms
, 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 twodimensional 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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Cited by 6 (4 self)
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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 twodimensional 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
 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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Cited by 35 (9 self)
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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 infinitedimensional 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
"... In this note we establish an existence and uniqueness result for the equation u − Au + F (u) = f where A is linear, quasipositive 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, quasipositive 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
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372