From dc62f3cc9c5a38f229a6a20a4cbf6112b4b921fb Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub@users.noreply.github.com>
Date: Mon, 25 Apr 2022 17:50:29 +0400
Subject: [PATCH 1/2] handle empty coeff vectors in Multiplication

---
 src/Spaces/Ultraspherical/UltrasphericalOperators.jl | 7 +++++--
 test/OperatorTest.jl                                 | 7 +++++++
 2 files changed, 12 insertions(+), 2 deletions(-)

diff --git a/src/Spaces/Ultraspherical/UltrasphericalOperators.jl b/src/Spaces/Ultraspherical/UltrasphericalOperators.jl
index 282d83d..a63117b 100644
--- a/src/Spaces/Ultraspherical/UltrasphericalOperators.jl
+++ b/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
diff --git a/test/OperatorTest.jl b/test/OperatorTest.jl
index 93d6ad1..a058aae 100644
--- a/test/OperatorTest.jl
+++ b/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

From b93a8fdd8f9c7671d40da704d9b84f2fe06d65a7 Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub@users.noreply.github.com>
Date: Tue, 26 Apr 2022 15:16:02 +0400
Subject: [PATCH 2/2] version bump to v0.4.8

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index aff6155..0810db5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.4.7"
+version = "0.4.8"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"