The standard Laplacian *-\triangle_{\mathbb R^n}* in *L^2(\mathbb R^n)* is self-adjoint and translation invariant on the finite-dimensional vector space *\mathbb R^n*. In this paper, using some quadratic form, we define a translation invariant operator *-\triangle_{\mathbb R^\infty}* on *\mathbb R^\infty* as a non-negative self-adjoint operator in some non-separable Hilbert space *L^2(\mathbb R^\infty)*,... Show more

August 15, 2024

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Self-adjoint Laplace operator with translation invariance on infinite-dimensional space $\mathbb R^\infty$

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