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In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two...
We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety in characteristic zero is determined by its arcs at a point. Using differential arcs, we show that if ( K , +, ×, δ 1 , . . ., δ n ) is a differentially closed field of...
Given 1 < p < 2, we construct a Banach function space with ॣ-order continuous norm which contains and has the property that the Fourier transform map has a continuous ℓ p ′ (ℤ)-valued extension to . Moreover, is maximal with these properties and satisfies with both containments proper....
We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.
We extend the symmetry result of Gidas-Ni-Nirenberg B. Gidas, W. M. Ni, L. Nirenberg , Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243. to semilinear polyharmonic Dirichlet problems in the unit ball. In the proof we develop a new variant of the...
In this paper we consider the constant term φ K ( y , s ) of the non-normalized Eisenstein series attached to PSL(2, K ), where K is either ℚ or an imaginary quadratic held of class number one. The main purpose of this paper is to show that for every a ≧ 1 the zeros of the Dirichlet series...
Let L / K be an extension of number fields where L /ℚ is abelian. We define such an extension to be Leopoldt if the ring of integers L of L is free over the associated order . Furthermore we define an abelian number field K to be Leopoldt if every finite extension L / K with L /ℚ abelian is...
We discuss finite Morse index solutions of –Δ u = f ( u ) on the whole space or half spaces and their application to bounded domain problems. Our main interest is to cases where the growth is faster than critical.
We formulate a comparison of minimal log discrepancies of a variety and its ambient space with appropriate boundaries in terms of motivic integration. It was obtained also by Ein and Mustaţă independently.
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