Results 281 to 290 of about 534,220 (309)
Quantum Dynamics Simulations of Exciton Polariton Transport. [PDF]
Nano LettChng BXK, Mondal ME, Ying W, Huo P.
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Embeddings of symmetric operator spaces into Lp-spaces, 1 ≤ p < 2, on finite von Neumann algebras
Jinghao Huang +3 more
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The Wave Equation in Lp-Spaces [PDF]
Semigroup Forum, 2005 In the first part of the paper, Gaussian estimates are used to study $L^p$-summability of the solution of the wave equation in $L^p(\Omega)$ associated with a general operator in divergence form with bounded coefficients. Secondly, we prove that if $\Omega$ is a cube in $\RR^N$, then the Laplacian with Dirichlet or Neumann boundary conditions generates
Valentin Keyantuo, Mahamadi Warma
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International Mathematics Research Notices, 2010
A representation theorem is established for continuous valuations on L p -spaces whose underlying measure is non-atomic. As a consequence, a complete classification is obtained of continuous translation invariant valuations on and of continuous rotation invariant valuations on L p (S n−1 ).2000 AMS subject classification: 46E30 (52B45)
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A representation theorem is established for continuous valuations on L p -spaces whose underlying measure is non-atomic. As a consequence, a complete classification is obtained of continuous translation invariant valuations on and of continuous rotation invariant valuations on L p (S n−1 ).2000 AMS subject classification: 46E30 (52B45)
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1998
The L p -spaces of functions the pth power of whose absolute value is integrable are introduced. Minkowski’s and Holder’s inequality are shown, and the L p -spaces are seen to be Banach spaces. Also, the approximation of Lp-functions by smooth ones is discussed. These mollifications are also used to show the existence of partitions of unity.
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The L p -spaces of functions the pth power of whose absolute value is integrable are introduced. Minkowski’s and Holder’s inequality are shown, and the L p -spaces are seen to be Banach spaces. Also, the approximation of Lp-functions by smooth ones is discussed. These mollifications are also used to show the existence of partitions of unity.
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1998
For (X, ℜ, μ) a positive measure space, it has already been noted that μ - a.e. equality is an equivalence relation, and the relation ≤ μ-a.e. a preorder, on.This section studies the structure of the equivalence classes into which μ-a,e. equality partitions.Since the set X/X( ℜ) is always u-null (2.7.7 a)), only the function values on the set X(ℜ) have
Corneliu Constantinescu +3 more
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For (X, ℜ, μ) a positive measure space, it has already been noted that μ - a.e. equality is an equivalence relation, and the relation ≤ μ-a.e. a preorder, on.This section studies the structure of the equivalence classes into which μ-a,e. equality partitions.Since the set X/X( ℜ) is always u-null (2.7.7 a)), only the function values on the set X(ℜ) have
Corneliu Constantinescu +3 more
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2002
Let { X,A,μ} be a measure space and let E be a measurable subset of X. A measurable function \(f:E \to {{\mathbb{R}}^{*}}\) is said to be in L P (E) for P≥1 if is integrable on E, i.e., if $$ \left\| f \right\|_p \mathop = \limits^{def} \left( {\smallint _E \left| f \right|^p d\mu } \right)^{1/p} < \infty $$ (1.1 ...
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Let { X,A,μ} be a measure space and let E be a measurable subset of X. A measurable function \(f:E \to {{\mathbb{R}}^{*}}\) is said to be in L P (E) for P≥1 if is integrable on E, i.e., if $$ \left\| f \right\|_p \mathop = \limits^{def} \left( {\smallint _E \left| f \right|^p d\mu } \right)^{1/p} < \infty $$ (1.1 ...
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, 1996 5.1 In this section we prove several fundamental inequalities. For example, if p, q, and r with 1/p + 1/q = 1/r belong to [0, +∞], and if f, g are two functions on Ω such that N p (f) and N q (g) are finite, then N r (fg) ≤ N p (f)N q (g) (Proposition 5.1.2).
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