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If the right-hand side <jats:italic>f<\/jats:italic> is a rapidly converging series of separable functions, the solution <jats:italic>u<\/jats:italic> can be represented in the same way. These constructions are based on approximations of the function 1\/<jats:italic>r<\/jats:italic> by sums of exponential functions. The aim of this paper is to prove results of similar kind for more general right-hand sides <jats:inline-formula><jats:alternatives><jats:tex-math>$$f(x)=F(Tx)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mrow>\n<mml:mi>f<\/mml:mi>\n<mml:mo>(<\/mml:mo>\n<mml:mi>x<\/mml:mi>\n<mml:mo>)<\/mml:mo>\n<mml:mo>=<\/mml:mo>\n<mml:mi>F<\/mml:mi>\n<mml:mo>(<\/mml:mo>\n<mml:mi>T<\/mml:mi>\n<mml:mi>x<\/mml:mi>\n<mml:mo>)<\/mml:mo>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> that are composed of a separable function on a space of a dimension <jats:italic>n<\/jats:italic> greater than <jats:italic>m<\/jats:italic> and a linear mapping given by a matrix <jats:italic>T<\/jats:italic> of full rank. These results are based on the observation that in the high-dimensional case, for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\omega $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mi>\u03c9<\/mml:mi>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> in most of the <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {R}}^n$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:msup>\n<mml:mrow>\n<mml:mi>R<\/mml:mi>\n<\/mml:mrow>\n<mml:mi>n<\/mml:mi>\n<\/mml:msup>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the euclidian norm of the vector <jats:inline-formula><jats:alternatives><jats:tex-math>$$T^t\\omega $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mrow>\n<mml:msup>\n<mml:mi>T<\/mml:mi>\n<mml:mi>t<\/mml:mi>\n<\/mml:msup>\n<mml:mi>\u03c9<\/mml:mi>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> in the lower dimensional space <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {R}}^m$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:msup>\n<mml:mrow>\n<mml:mi>R<\/mml:mi>\n<\/mml:mrow>\n<mml:mi>m<\/mml:mi>\n<\/mml:msup>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> behaves like the euclidian norm of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\omega $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mi>\u03c9<\/mml:mi>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00211-020-01138-8","type":"journal-article","created":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T06:10:04Z","timestamp":1596175804000},"page":"219-238","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the expansion of solutions of Laplace-like equations into traces of separable higher dimensional functions"],"prefix":"10.1007","volume":"146","author":[{"given":"Harry","family":"Yserentant","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"1138_CR1","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1093\/imanum\/dri015","volume":"25","author":"D Braess","year":"2005","unstructured":"Braess, D., Hackbusch, W.: Approximation of $$1\/x$$ by exponential sums in $$[1,\\infty )$$. 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