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Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model. [PDF]
J Phys Chem ABakkestuen VH +5 more
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On additive and multiplicative Hilbert cubes
Journal of Combinatorial Theory - Series A, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Norbert Hegyvári
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On Hilbert Cubes in Certain Sets
The Ramanujan Journal, 1999Given \(k\geq 1\), a set \(H\subset \mathbb{N}\) is called a cube of size \(k\) if there exist \(a>0\) and \(x_1,\dots,x_k\) such that \(H=\{a+\sum_{i=1}^k\varepsilon_ix_i:\varepsilon=0\text{ or }1\}\). If the set of \(x\)'s is infinite the cube is called infinite.
Hegyvári, N., Sárközy, A.
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Homogeneity of the Hilbert Cube
UniversitextAlejandro Illanes, Illanes Alejandro
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MANIFOLDS MODELED BY AN EQUIVARIANT HILBERT CUBE
Russian Academy of Sciences. Sbornik Mathematics, 1995An equivariant analog of the theory of \(Q\)-manifolds is constructed in the paper. Given a compact group \(G\), the author defines an ``equivariant'' Hilbert cube \(\mathbb{Q}\) as the countable power of the product \(\Pi_\rho D_\rho\) of the unit balls of all irreducible orthogonal representations of \(G\).
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Characterizations of Hilbert Manifolds and Hilbert Cube Manifolds
2020In this chapter, we prove the Torunczyk characterizations of Hilbert manifolds (non-separable Hilbert spaces are also considered as model spaces) and Hilbert cube manifolds. By using the characterization of Hilbert space, we show that every Frechet space is homeomorphic to Hilbert space with the same weight. Additionally, it is shown that if X is a non-
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Publicationes Mathematicae Debrecen, 2008
Summary: Given a subset \(E\) of the set of natural numbers, \(FS(E)\) is defined as the collection of all sums of elements of finite subsets of \(E\) and any translation of \(FS(E)\) is said to be a Hilbert cube. We estimate the rate of growth of \(E\) given that \(FS(E)\) avoids a set of multiplies of a given infinite set of primes.
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Summary: Given a subset \(E\) of the set of natural numbers, \(FS(E)\) is defined as the collection of all sums of elements of finite subsets of \(E\) and any translation of \(FS(E)\) is said to be a Hilbert cube. We estimate the rate of growth of \(E\) given that \(FS(E)\) avoids a set of multiplies of a given infinite set of primes.
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Ulam’s Conjecture on Invariance of Measure in the Hilbert Cube
Frontiers in Mathematics, 2023Soon-Mo Jung
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