handle empty coeff vectors in Multiplication

Author: jishnub

src/Spaces/Ultraspherical/UltrasphericalOperators.jl

@@ -31,8 +31,11 @@ function Multiplication(f::Fun{C},sp::Ultraspherical{Int}) where C<:Chebyshev
     if order(sp) == 1
         cfs = f.coefficients
         MultiplicationWrapper(f,
-            SpaceOperator(SymToeplitzOperator(cfs/2) +
-                                HankelOperator(view(cfs,3:length(cfs))/(-2)),
+            SpaceOperator(
+                length(cfs) > 0 ?
+                    SymToeplitzOperator(cfs/2) +
+                        HankelOperator(view(cfs,3:length(cfs))/(-2)) :
+                    HankelOperator(view(cfs,3:length(cfs))/(-2)),
                           sp,sp))
 
     else

test/OperatorTest.jl

@@ -268,6 +268,13 @@ import ApproxFunOrthogonalPolynomials: JacobiZ
         @test exp(-M).f == Multiplication(exp(-x), Chebyshev()).f
         @test (M/3).f == (3\M).f == Multiplication(x/3, Chebyshev()).f
         @test (M*3).f == (3*M).f == Multiplication(x*3, Chebyshev()).f
+
+        # test for Fun with an empty coefficients vector
+        v1 = Fun(Chebyshev(), Float64[])
+        v2 = Fun(Chebyshev(), Float64[0.0])
+        sp = Ultraspherical(1)
+        # the matrix representations should be identical
+        @test Multiplication(v1, sp)[1:4, 1:4] == Multiplication(v2, sp)[1:4, 1:4]
     end
 
     @testset "lastindex" begin