What is recorded here?
For every prescribed triangular array of distinct interpolation nodes in a real compact interval, some continuous function fails to be uniformly approximated by its Lagrange interpolation polynomials. Faber proves the corresponding periodic trigonometric obstruction and derives unbounded interpolation-operator norms, using a constructive continuous-function argument.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
Uniform-convergence failure is the retained result: no claim of divergence everywhere or unboundedness at a single fixed point for every node array. Nodes are fixed independently of the function. This does not forbid adaptive interpolation, approximation without interpolation, or arbitrary polynomial Schauder systems with unrestricted degrees. The algebraic conclusion is original p208, and the periodic proof conclusion is p199. No assertion of divergence at every point or one fixed point for every array. Adaptive nodes, noninterpolatory approximation and unrestricted-degree polynomial systems are not ruled out. Adjacent Blaschke paper and preceding article excluded.
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People and systems
Georg Faber
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
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English catalogue narrative
Faber's obstruction to universal uniform polynomial interpolation
For every prescribed triangular array of distinct interpolation nodes in a real compact interval, some continuous function fails to be uniformly approximated by its Lagrange interpolation polynomials. Faber proves the corresponding periodic trigonometric obstruction and derives unbounded interpolation-operator norms, using a constructive continuous-function argument.
Scientific scope
Uniform-convergence failure is the retained result: no claim of divergence everywhere or unboundedness at a single fixed point for every node array. Nodes are fixed independently of the function. This does not forbid adaptive interpolation, approximation without interpolation, or arbitrary polynomial Schauder systems with unrestricted degrees. The algebraic conclusion is original p208, and the periodic proof conclusion is p199. No assertion of divergence at every point or one fixed point for every array. Adaptive nodes, noninterpolatory approximation and unrestricted-degree polynomial systems are not ruled out. Adjacent Blaschke paper and preceding article excluded.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Georg Faber
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.