On some spaces of functions and distributions (I). Spaces $D_{M}$ and $D^{\prime }_{M}$

J. Musielak

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Contribution to the theory of Saks spaces

W. Orlicz (1957)

Fundamenta Mathematicae

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Reflexivity and summability: the Nakano $l (p_{i})$ spaces

D. Waterman, T. Ito, F. Barber, J. Ratti (1969)

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Linear functionals on two-norm spaces

A. Alexiewicz, Z. Semadeni (1958)

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The Fredholm Theory of Linear Equations in Banach spaces

T. Leżański (1953)

Studia Mathematica

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Linear operations in Saks spaces (II)

W. Orlicz (1955)

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Truncations of Gauss' square exponent theorem

Ji-Cai Liu, Shan-Shan Zhao (2022)

Czechoslovak Mathematical Journal

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We establish two truncations of Gauss’ square exponent theorem and a finite extension of Euler’s identity. For instance, we prove that for any positive integer $n$ , $\sum_{k = 0}^{n} {(- 1)}^{k} [\begin{matrix} 2 n - k \\ k \end{matrix}] {(q; q^{2})}_{n - k} q^{(\binom{k + 1}{2})} = \sum_{k = - n}^{n} {(- 1)}^{k} q^{k^{2}},$ where $[\begin{matrix} n \\ m \end{matrix}] = \prod_{k = 1}^{m} \frac{1 - q^{n - k + 1}}{1 - q^{k}} and {(a; q)}_{n} = \prod_{k = 0}^{n - 1} (1 - a q^{k}) .$

On decompositions in generalised Lorentz-Zygmund spaces

J. S. Neves (2001)

Bollettino dell'Unione Matematica Italiana

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Il lavoro presenta diverse caratterizzazioni degli spazi Lorentz-Zygmund generalizzati (GLZ) $L_{p, q; α} (R)$ , con $p, q \in (0, + \infty]$ , $m \in N$ , $α \in R^{m}$ e $(R, μ)$ spazio misurato con misura $μ (R)$ finita. Dato uno spazio misurato $(R, μ)$ e $α \in R_{-}^{m}$ , otteniamo representazioni equivalenti per la (quasi-) norma dello spazio GLZ $L_{\infty, \infty; α} (R)$ . Inoltre, se $(R, μ)$ è uno spazio misurato con misura finita e $α \in R_{+}^{m}$ , viene presentata in termini di decomposizioni una norma equivalente per lo spazio $L_{1, 1; α} (R)$ . Si dimostra che le norme equivalenti considerate per $L_{\infty, \infty; α} (R)$ , con $(R, μ)$ uno spazio a misura...

On summability of double sequences (II)

A. Alexiewicz, W. Orlicz (1959)

Annales Polonici Mathematici

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On Leżański's determinants of linear equations in Banach spaces

R. Sikorski (1953)

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Summability in $ł (p_{1}, p_{2}, . . .)$ spaces

V. Klee (1965)

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Displaying similar documents to “On some spaces of functions and distributions (I). Spaces D M and D M ' ”

Displaying similar documents to “On some spaces of functions and distributions (I). Spaces $D_{M}$ and $D_{M}^{'}$ ”